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Net Spaces in Categorical Topology a
Author(s) -
ŠLAPAL JOSEF
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb49183.x
Subject(s) - net (polyhedron) , topological space , generalization , categorical variable , mathematics , axiom , separation axiom , cartesian closed category , construct (python library) , topology (electrical circuits) , compact open topology , pure mathematics , discrete mathematics , topological tensor product , computer science , functional analysis , combinatorics , geometry , mathematical analysis , biochemistry , statistics , chemistry , gene , programming language
In the paper we introduce the notion of S ‐nets, S a nonempty construct, as a generalization of the usual nets. S ‐net spaces and continuous maps between them are then defined in a natural way. For S ‐net spaces we introduce a number of axioms and study the categories obtained. We find some topological and Cartesian closed categories of S ‐net spaces and describe their relations to certain known topological categories.