A note on topological model theory
Abraham Robinson (1974)
Fundamenta Mathematicae
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Abraham Robinson (1974)
Fundamenta Mathematicae
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H.-H. Herda, R. C. Metzler (1966)
Colloquium Mathematicae
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Tomasz Witczak (2019)
Bulletin of the Section of Logic
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We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.
Sikorski, R.
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Čech, Eduard, Frolík, Zdeněk, Katětov, Miroslav
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Dutta, Tapas (1986)
International Journal of Mathematics and Mathematical Sciences
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Hidemitsu Sayeki (1967)
Fundamenta Mathematicae
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Spira, Robert (1967)
Portugaliae mathematica
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Karol Borsuk (1959)
Fundamenta Mathematicae
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Artur Piękosz (2013)
Annales Polonici Mathematici
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We begin a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings. We reformulate the axioms. Generalized topology is found to be connected with the concept of a bornological universe. Both GTS and its full subcategory SS of small spaces are topological categories. The second part of this paper will also appear in this journal.