Publication detail

Neighborhoods and convergence with respect to a closure operator

ŠLAPAL, J.

Czech title

Okolí a konvergence vzhledem k uzávěrovému operátoru

English title

Neighborhoods and convergence with respect to a closure operator

Type

journal article - other

Language

en

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.

Czech abstract

Jsou studována okolí a konvergence vzhledem ke kategoriálnímu uzávěrovému operátoru. Zejména je diskutovány saparace a kompaktnost získané pomocí okolí obvyklým způsobem, které jsou porovnány s obvyklou separací a kompaktností. Je také zaveden a studován pojem konvergence založený na využití centrovaných systémů podobjektů, která přirozeným způsobem zobecňuje topologockou konvergenci využívající filtrů . also introduce a concept of convergence based on using centered

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 in Czech

Okolí, konvergence, uzávěrový operátor

Keywords in English

Neighborhoods, convergence, closure operator

RIV year

2011

Released

25.08.2011

ISSN

0139-9918

Journal

Mathematica Slovaca

Volume

61

Number

5

Pages from–to

717–732

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",
  month="August",
  pages="717--732",
  issn="0139-9918"
}