Publication detail
Categorical neighborhood operators
ŠLAPAL, J. HOLGATE, D.
Czech title
Kategoriální operátory okolí
English title
Categorical neighborhood operators
Type
journal article - other
Language
en
Original 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.
Czech abstract
V práci jsou je definován a studován pojem operátoru okolí na kategoriích. Tento operátor je dafinován tak, že každému podobjektu libovolného objektu je pořiřazen vhodně axiomatizovaný stack podobjektů. Jsou diskutovány uzávěrové operátory, operátory vnitřku, konvergence a některé další pojmy vzhledem k danému oparátoru okolí.
English 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 in Czech
Kategorie, faktorizační systém, uzávěrový operátor, konvergence, kompaktnost
Keywords in English
Category, factorization system, closure operator, neighborhood operator, convergence, separation, compactness
RIV year
2011
Released
07.09.2011
ISSN
0166-8641
Journal
Topology and its Applications
Volume
158
Number
16
Pages from–to
2356–2365
Pages count
10
BIBTEX
@article{BUT73395,
author="Josef {Šlapal} and David {Holgate},
title="Categorical neighborhood operators",
journal="Topology and its Applications",
year="2011",
volume="158",
number="16",
month="September",
pages="2356--2365",
issn="0166-8641"
}