Displaying similar documents to “Topological spaces”

Topology from Neighbourhoods

Roland Coghetto (2015)

Formalized Mathematics

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Using Mizar [9], and the formal topological space structure (FMT_Space_Str) [19], we introduce the three U-FMT conditions (U-FMT filter, U-FMT with point and U-FMT local) similar to those VI, VII, VIII and VIV of the proposition 2 in [10]: If to each element x of a set X there corresponds a set B(x) of subsets of X such that the properties VI, VII, VIII and VIV are satisfied, then there is a unique topological structure on X such that, for each x ∈ X, B(x) is the set of neighborhoods...

On generalized topological spaces I

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.