A conglomerate of exponential supercategories of the category of finitely generated topological spaces
type: Item
instance of: scholarly article
title: A conglomerate of exponential supercategories of the category of finitely generated topological spaces
zbMATH Open document ID: 0814.18001
DOI: 10.1007/BF01827932
published in: Aequationes Mathematicae
publication date: 1995-06-12T00:00:00Z
full work available at URL: https://eudml.org/doc/182475
review text: The author calls a full extension \({\mathcal B}\) of a category \({\mathcal A}\) an exponential supercategory of \({\mathcal A}\) provided that \({\mathcal B}\) has finite products and for each \({\mathcal B}\)-object \(B\) and each \({\mathcal A}\)- object \(A\) the functor \(B \times_ - : {\mathcal B} \to {\mathcal B}\) has a couniversal arrow \(B \times A^ B \to A\) for \(A\) with \(A^ B\) in \({\mathcal A}\). He considers the category \({\mathcal A}\) of finitely generated topological spaces as a full subcategory of the category \({\mathcal P} r{\mathcal T} op\) of pretopological spaces, and constructs, for each ordinal \(\alpha\), an exponential supercategory \({\mathcal B}_ \alpha\) of \({\mathcal A}\) in \({\mathcal P} r{\mathcal T}op\).
Mathematics Subject Classification ID: 18B15
Mathematics Subject Classification ID: 18D15
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 729149
zbMATH Keywords: function space
zbMATH Keywords: exponential object
zbMATH Keywords: Cartesian-closedness
zbMATH Keywords: pretopological spaces
author: Josef Šlapal
reviewed by: Horst Herrlich
MaRDI profile type: Publication
cites work: Q5516652
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cites work: Notes on Topological Spaces with Minimum Neighborhoods
cites work: CARTESIAN CLOSED COREFLECTIVE HULLS
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cites work: Cartesian closedness in categories of relational systems
OpenAlex ID: W4246504687
description: scientific article; zbMATH DE number 729149