Result Details
Neighborhoods and convergence with respect to a closure operator
ŠLAPAL, J. Neighborhoods and convergence with respect to a closure operator. Mathematica Slovaca, 2011, vol. 61, no. 5, p. 717-732. ISSN: 0139-9918.
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc., IM (FME)
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
Published
2011
Pages
717–732
Journal
Mathematica Slovaca, vol. 61, no. 5, ISSN 0139-9918
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"
}
Departments