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  1. Robin Havea, Hajime Ishihara & Luminita Vîta (2008). Separation Properties in Neighbourhood and Quasi-Apartness Spaces. 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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  2. Hajime Ishihara, Ray Mines, Peter Schuster & Luminiţa Vîţă (2006). Quasi-Apartness and Neighbourhood Spaces. 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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  3. Luminiţa Simona Vîţă (2006). Extending Strongly Continuous Functions Between Apartness Spaces. 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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  4. Douglas Bridges, Hajime Ishihara, Peter Schuster & Luminiţa Vîţa (2005). Strong Continuity Implies Uniform Sequential Continuity. Archive for Mathematical Logic 44 (7):887-895.
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  5. Douglas Bridges & Luminiţa Vîţă (2004). Corrigendum to "a Proof-Technique in Uniform Space Theory". Journal of Symbolic Logic 69 (1):328-328.
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  6. 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.
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  7. Luminita Simona Vîta (2003). On Proximal Convergence in Uniform Spaces. 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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  8. Luminita Simona Vîta (2003). Proximal and Uniform Convergence on Apartness Spaces. 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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  9. Douglas Bridges, Peter Schuster & Luminiţa Vîţă (2002). Apartness, Topology, and Uniformity: A Constructive View. Mathematical Logic Quarterly 48 (S1):16-28.
    The theory of apartness spaces, and their relation to topological spaces and uniform spaces , 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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  10. Luminita Simona Vîta, D. Bridges & P. Schuster (2002). Apartness, Topology, and Uniformity: A Constructive View: A Constructive View. Mathematical Logic Quarterly 48:16-28.
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  11. D. Bridges & Luminita Simona Vîta (2001). Characterising Near Continuity Constructively. 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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