Publication result detail

Neighborhoods and convergence with respect to a closure operator

ŠLAPAL, J.

Original Title

Neighborhoods and convergence with respect to a closure operator

English Title

Neighborhoods and convergence with respect to a closure operator

Type

Peer-reviewed article not indexed in WoS or Scopus

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.

English 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

Key words in English

Neighborhoods, convergence, closure operator

Authors

ŠLAPAL, J.

RIV year

2012

Released

25.08.2011

ISBN

0139-9918

Periodical

Mathematica Slovaca

Volume

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"
}