Result Details

Categorical neighborhood operators

ŠLAPAL, J.; HOLGATE, D. Categorical neighborhood operators. TOPOLOGY AND ITS APPLICATIONS, 2011, vol. 158, no. 16, p. 2356-2365. ISSN: 0166-8641.

Type

journal article

Language

English

Authors

Šlapal Josef, prof. RNDr., CSc., IM (FME)
Holgate David, Prof.

Abstract

We introduce and study a
concept of neighborhood operator on a category. Such an operator is
obtained by assigning a suitably axiomatized stack of subobjects --
the neighbourhoods -- to every subobject of each object in the
category. We discuss closure and interior operators, convergence,
separation and compactness with respect to a neighborhood operator,
defined in a natural way.

Keywords

Category, factorization system, closure operator, neighborhood operator, convergence, separation, compactness

Published

2011

Pages

2356–2365

Journal

TOPOLOGY AND ITS APPLICATIONS, vol. 158, no. 16, ISSN 0166-8641

BibTeX

@article{BUT73395,
  author="Josef {Šlapal} and David {Holgate}",
  title="Categorical neighborhood operators",
  journal="TOPOLOGY AND ITS APPLICATIONS",
  year="2011",
  volume="158",
  number="16",
  pages="2356--2365",
  issn="0166-8641"
}

Departments

Institute of Mathematics (IM)