47 found
Sort by:
Disambiguations:
Douglas S. Bridges [25]Douglas Bridges [22]
  1. Douglas S. Bridges (2013). Characterising Dominated Weak-Operator Continuous Functionals on Subspaces Of. Annals of Pure and Applied Logic 164 (4):416-420.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  2. Douglas S. Bridges, Hajime Ishihara & Maarten McKubre‐Jordens (2013). Uniformly Convex Banach Spaces Are Reflexive—Constructively. Mathematical Logic Quarterly 59 (4-5):352-356.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  3. Douglas S. Bridges (2012). Almost New Pre-Apartness From Old. Annals of Pure and Applied Logic 163 (8):1009-1015.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  4. Douglas S. Bridges (2012). Compactness Notions for an Apartness Space. Archive for Mathematical Logic 51 (5):517-534.
    Two new notions of compactness, each classically equivalent to the standard classical one of sequential compactness, for apartness spaces are examined within Bishop-style constructive mathematics.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  5. Douglas S. Bridges (2012). How to Construct a Product of a‐Frames. Mathematical Logic Quarterly 58 (4‐5):281-293.
    No categories
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  6. Douglas S. Bridges (2012). Reflections on Function Spaces. Annals of Pure and Applied Logic 163 (2):101-110.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  7. Douglas S. Bridges & Robin S. Havea (2012). Square Roots and Powers in Constructive Banach Algebra Theory. In. In S. Barry Cooper (ed.), How the World Computes. 68--77.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  8. Douglas S. Bridges & Hannes Diener (2010). The Anti-Specker Property, Positivity, and Total Boundedness. Mathematical Logic Quarterly 56 (4):434-441.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  9. Douglas S. Bridges & Iris Loeb (2010). Glueing Continuous Functions Constructively. Archive for Mathematical Logic 49 (5):603-616.
    The glueing of (sequentially, pointwise, or uniformly) continuous functions that coincide on the intersection of their closed domains is examined in the light of Bishop-style constructive analysis. This requires us to pay attention to the way that the two domains intersect.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  10. Douglas Bridges & Matthew Hendtlass (2010). Continuous Homomorphisms of R Onto a Compact Group. Mathematical Logic Quarterly 56 (2):191-197.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  11. Douglas Bridges & Matthew Hendtlass (2010). Continuous Isomorphisms From R Onto a Complete Abelian Group. Journal of Symbolic Logic 75 (3):930-944.
    This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of R onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if G is a complete (metric) abelian group that is the range of a continuous isomorphism from R, then G is noncompact. A special case occurs when G satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective mappings (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  12. Douglas S. Bridges (2009). Constructive Notions of Equicontinuity. Archive for Mathematical Logic 48 (5):437-448.
    In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  13. Josef Berger & Douglas Bridges (2008). The Anti-Specker Property, a Heine–Borel Property, and Uniform Continuity. Archive for Mathematical Logic 46 (7-8):583-592.
    Working within Bishop’s constructive framework, we examine the connection between a weak version of the Heine–Borel property, a property antithetical to that in Specker’s theorem in recursive analysis, and the uniform continuity theorem for integer-valued functions. The paper is a contribution to the ongoing programme of constructive reverse mathematics.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  14. Douglas Bridges, Constructive Mathematics. Stanford Encyclopedia of Philosophy.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  15. Douglas S. Bridges (2008). Product a-Frames and Proximity. Mathematical Logic Quarterly 54 (1):12-26.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  16. Douglas S. Bridges (2008). Uniform Continuity Properties of Preference Relations. Notre Dame Journal of Formal Logic 49 (1):97-106.
    The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara's principle BD-ℕ implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  17. Douglas S. Bridges (2007). Constructing Local Optima on a Compact Interval. Archive for Mathematical Logic 46 (2):149-154.
    The existence of either a maximum or a minimum for a uniformly continuous mapping f of a compact interval into ${\mathbb{R}}$ is established constructively under the hypotheses that f′ is sequentially continuous and f has at most one critical point.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  18. Douglas Bridges & Hannes Diener (2007). The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem. Journal of Symbolic Logic 72 (4):1379 - 1384.
    We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every pointwise continuous mapping of [0, 1] into R is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideas.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  19. Josef Berger, Douglas Bridges & Peter Schuster (2006). The Fan Theorem and Unique Existence of Maxima. Journal of Symbolic Logic 71 (2):713 - 720.
    The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  20. Douglas S. Bridges (2006). Church's Thesis and Bishop's Constructivism. In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. 1--58.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  21. Douglas Bridges & Hannes Diener (2006). A Constructive Treatment of Urysohn's Lemma in an Apartness Space. Mathematical Logic Quarterly 52 (5):464-469.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  22. Douglas Bridges, Hajime Ishihara, Peter Schuster & Luminiţa Vîţa (2005). Strong Continuity Implies Uniform Sequential Continuity. Archive for Mathematical Logic 44 (7):887-895.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  23. Douglas Bridges & Luminiţa Vîţă (2004). Corrigendum to "a Proof-Technique in Uniform Space Theory". Journal of Symbolic Logic 69 (1):328-328.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  24. Douglas Bridges & Luminiţa Vîţă (2003). A Proof-Technique in Uniform Space Theory. Journal of Symbolic Logic 68 (3):795-802.
    In the constructive theory of uniform spaces there occurs a technique of proof in which the application of a weak form of the law of excluded middle is circumvented by purely analytic means. The essence of this proof-technique is extracted and then applied in several different situations.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  25. Douglas Bridges (2002). Review: Oliver Aberth, Computable Calculus. [REVIEW] Bulletin of Symbolic Logic 8 (3):426-428.
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  26. Douglas Bridges, Peter Schuster & Luminiţa Vîţă (2002). Apartness, Topology, and Uniformity: A Constructive View. Mathematical Logic Quarterly 48 (S1):16-28.
    No categories
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  27. Douglas Bridges & Ayan Mahalanobis (2001). Bounded Variation Implies Regulated: A Constructive Proof. Journal of Symbolic Logic 66 (4):1695-1700.
    It is shown constructively that a strongly extensional function of bounded variation on an interval is regulated, in a sequential sense that is classically equivalent to the usual one.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  28. Douglas Bridges & Ayan Mahalanobis (2000). Sequential Continuity of Functions in Constructive Analysis. Mathematical Logic Quarterly 46 (1):139-143.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  29. Douglas S. Bridges (1999). Can Constructive Mathematics Be Applied in Physics? Journal of Philosophical Logic 28 (5):439-453.
    The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.
    Direct download (8 more)  
     
    My bibliography  
     
    Export citation  
  30. Douglas Bridges & Luminita Dediu (1999). Weak-Operator Continuity and the Existence of Adjoints. Mathematical Logic Quarterly 45 (2):203-206.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  31. Douglas Bridges & Steeve Reeves (1999). Constructive Mathematics in Theory and Programming Practice. Philosophia Mathematica 7 (1):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  32. Douglas Bridges, Fred Richman & Peter Schuster (1999). Linear Independence Without Choice. Annals of Pure and Applied Logic 101 (1):95-102.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  33. Douglas Bridges (1998). Constructive Truth in Practice. In H. G. Dales & Gianluigi Oliveri (eds.), Truth in Mathematics. Oxford University Press, Usa. 53--69.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  34. Douglas Bridges & Hajime Ishihara (1998). A Definitive Constructive Open Mapping Theorem? Mathematical Logic Quarterly 44 (4):545-552.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  35. Douglas Bridges & Ray Mines (1998). Sequentially Continuous Linear Mappings in Constructive Analysis. Journal of Symbolic Logic 63 (2):579-583.
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  36. Douglas S. Bridges (1995). Constructive Mathematics and Unbounded Operators — a Reply to Hellman. Journal of Philosophical Logic 24 (5):549 - 561.
    It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  37. Douglas S. Bridges & Hajime Ishihara (1994). Complements of Intersections in Constructive Mathematics. Mathematical Logic Quarterly 40 (1):35-43.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  38. Douglas Bridges & Hajime Ishihara (1994). Absolute Continuity and the Uniqueness of the Constructive Functional Calculus. Mathematical Logic Quarterly 40 (4):519-527.
    No categories
    Direct download (5 more)  
     
    My bibliography  
     
    Export citation  
  39. Douglas S. Bridges (1993). Constructive Notions of Strict Convexity. Mathematical Logic Quarterly 39 (1):295-300.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  40. Douglas S. Bridges (1993). Sequential, Pointwise, and Uniform Continuity: A Constructive Note. Mathematical Logic Quarterly 39 (1):55-61.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  41. Douglas S. Bridges (1989). A General Constructive Intermediate Value Theorem. Mathematical Logic Quarterly 35 (5):433-435.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  42. Douglas Bridges, William Julian & Ray Mines (1989). A Constructive Treatment of Open and Unopen Mapping Theorems. Mathematical Logic Quarterly 35 (1):29-43.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  43. Douglas S. Bridges (1979). A Criterion for Compactness in Metric Spaces? Mathematical Logic Quarterly 25 (7‐12):97-98.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  44. Douglas S. Bridges (1979). Geometric Intuition and Elementary Constructive Analysis. Zeitschrift für Mathematische Logik Und Grundlagen der Mathematik 25 (33):521-523.
    No categories
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  45. Douglas S. Bridges (1979). On the Constructive Convergence of Series of Independent Functions. Mathematical Logic Quarterly 25 (3‐6):93-96.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  46. Douglas S. Bridges (1978). A Note on Morse's Lambda‐Notation in Set Theory. Mathematical Logic Quarterly 24 (8):113-114.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  47. Douglas S. Bridges (1978). On Weak Operator Compactness of the Unit Ball of L(H). Mathematical Logic Quarterly 24 (31‐36):493-494.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation