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Publication detail
ŠLAPAL, J.
Original Title
Neighborhoods and convergence with respect to a closure operator
Type
journal article - other
Language
English
Original Abstract
We study neighborhoods with respect to a categorical closure operator. In particular, we discuss separation and compactness obtained from neighborhoods in a natural way and compare them with the usual closure separation and closure compactness. We also introduce a concept of convergence based on using centered systems of subobjects, which naturally generalizes the classical filter convergence in topological spaces. We investigate behavior of the convergence introduced and show, among others, that it relates to the separation and compactness in natural ways.
Keywords
Neighborhoods, convergence, closure operator
Authors
RIV year
2011
Released
25. 8. 2011
ISBN
0139-9918
Periodical
Mathematica Slovaca
Year of study
61
Number
5
State
Slovak Republic
Pages from
717
Pages to
732
Pages count
16
BibTex
@article{BUT47016, author="Josef {Šlapal}", title="Neighborhoods and convergence with respect to a closure operator", journal="Mathematica Slovaca", year="2011", volume="61", number="5", pages="717--732", issn="0139-9918" }