A categorical approach to absolute closure

G. Castellini; D. Holgate

doi:10.1007/s10474-009-9066-1

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Acta Mathematica Hungarica

Volume/Issue:: Volume 126: Issue 4

A categorical approach to absolute closure

Authors:

G. Castellini

G. Castellini University of Puerto Rico Department of Mathematical Sciences Mayagüez campus P.O. Box 9018 Mayagüez PR 00681-9018 USA

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and

D. Holgate

D. Holgate University of Stellenbosch Department of Mathematical Sciences Stellenbosch 7600 South Africa

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Pages:: 295–314

Online Publication Date:: 18 Dec 2009

Publication Date:: 01 Mar 2010

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10474-009-9066-1

Keywords:: closure operator; Galois connection; absolute closure compactness; 18A05; 06A15

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Abstract

Notions of strongly and absolutely closed objects with respect to a closure operator X on an arbitrary category X and with respect to a subcategory Y are introduced. This yields two Galois connections between closure operators on a given category X and subclasses of X, whose fixed points are studied. A relationship with some compactness notions is shown and examples are provided.

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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)