Acta Mathematica Hungarica
Volume/Issue:
Volume 124: Issue 1-2
Neighborhoods with respect to a categorical closure operator
Authors:
E. Giuli Universitá di L’Aquila Dipartimento di Matematica 67100 L’Aquila Italy

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J. Šlapal Brno University of Technology Department of Mathematics 616 69 Brno Czech Republic

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Pages:
1–14
Online Publication Date:
06 Jul 2009
Publication Date:
01 Jul 2009
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-009-8108-z
Keywords:
categorical closure operator; neighborhood; separation; compactness; primary 18D35; secondary 54A05, 54B30
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Abstract  

We introduce and study a concept of neighborhoods with respect to a categorical closure operator. The concept, which is based on using pseudocomplements in subobject lattices, naturally generalizes the classical neighborhoods in topological spaces and we show that it behaves accordingly. We investigate also separation and compactness defined in a natural way by the help of the neighboorhoods introduced.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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