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Luminiţa Vîţă [8]Luminiţa Simona Vîţă [3]
  1.  15
    Apartness Spaces as a Framework for Constructive Topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
    An axiomatic development of the theory of apartness and nearness of a point and a set is introduced as a framework for constructive topology. Various notions of continuity of mappings between apartness spaces are compared; the constructive independence of one of the axioms from the others is demonstrated; and the product apartness structure is defined and analysed.
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  2.  23
    Strong Continuity Implies Uniform Sequential Continuity.Douglas Bridges, Hajime Ishihara, Peter Schuster & Luminiţa Vîţa - 2005 - Archive for Mathematical Logic 44 (7):887-895.
    Uniform sequential continuity, a property classically equivalent to sequential continuity on compact sets, is shown, constructively, to be a consequence of strong continuity on a metric space. It is then shown that in the case of a separable metric space, uniform sequential continuity implies strong continuity if and only if one adopts a certain boundedness principle that, although valid in the classical, recursive and intuitionistic setting, is independent of Heyting arithmetic.
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  3.  17
    Quasi-Apartness and Neighbourhood Spaces.Hajime Ishihara, Ray Mines, Peter Schuster & Luminiţa Vîţă - 2006 - Annals of Pure and Applied Logic 141 (1):296-306.
    We extend the concept of apartness spaces to the concept of quasi-apartness spaces. We show that there is an adjunction between the category of quasi-apartness spaces and the category of neighbourhood spaces, which indicates that quasi-apartness is a more natural concept than apartness. We also show that there is an adjoint equivalence between the category of apartness spaces and the category of Grayson’s separated spaces.
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  4.  35
    Apartness, Topology, and Uniformity: A Constructive View.Douglas Bridges, Peter Schuster & Luminiţa Vîţă - 2002 - Mathematical Logic Quarterly 48 (4):16-28.
    The theory of apartness spaces, and their relation to topological spaces (in the point–set case) and uniform spaces (in the set–set case), is sketched. New notions of local decomposability and regularity are investigated, and the latter is used to produce an example of a classically metrisable apartness on R that cannot be induced constructively by a uniform structure.
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  5.  11
    Proximal and Uniform Convergence on Apartness Spaces.Luminiţa Simona Vîţă - 2003 - Mathematical Logic Quarterly 49 (3):255.
    The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity.
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  6.  37
    A Proof–Technique in Uniform Space Theory.Douglas Bridges & Luminiţa Vîţă - 2003 - 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.
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  7.  17
    Characterising Near Continuity Constructively.Douglas Bridges & Luminiţa Vîţă - 2001 - Mathematical Logic Quarterly 47 (4):535-538.
    The relation between near continuity and sequential continuity for mappings between metric spaces is explored constructively. It is also shown that the classical implications “near continuity implies sequential continuity” and “near continuity implies apart continuity” are essentially nonconstructive.
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  8.  1
    A Proof—Technique In Uniform Space Theory.Douglas Bridges & Luminiţa Vîţă - 2003 - 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.
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  9.  8
    Separation Properties in Neighbourhood and Quasi-Apartness Spaces.Robin Havea, Hajime Ishihara & Luminiţa Vîţă - 2008 - Mathematical Logic Quarterly 54 (1):58-64.
    We investigate separation properties for neighbourhood spaces in some details within a framework of constructive mathematics, and define corresponding separation properties for quasi-apartness spaces. We also deal with separation properties for spaces with inequality.
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  10.  15
    Extending Strongly Continuous Functions Between Apartness Spaces.Luminiţa Simona Vîţă - 2006 - Archive for Mathematical Logic 45 (3):351-356.
    A natural extension theorem for strongly continuous mappings, the morphisms in the category of apartness spaces, is proved constructively.
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  11.  5
    On Proximal Convergence in Uniform Spaces.Luminiţa Simona Vîţă - 2003 - Mathematical Logic Quarterly 49 (6):550.
    The paper deals with proximal convergence and Leader's theorem, in the constructive theory of uniform apartness spaces.
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