Almost reflective subcategories of \(\mathbf T \mathbf o \mathbf p\)
type: Item
instance of: scholarly article
title: Almost reflective subcategories of \(\mathbf T \mathbf o \mathbf p\)
zbMATH Open document ID: 0805.54016
DOI: 10.1016/0166-8641(93)90115-T
author: Horst Herrlich
published in: Topology and its Applications
publication date: 1993-06-29T00:00:00Z
review text: The paper deals with the relationship between almost reflective subcategories (= weakly reflective plus closed under the formation of retracts) and implicational subcategories (= injectivity classes in the sense of [\textit{J. Adámek} and \textit{J. Rosický}, Trans. Am. Math. Soc. 336, 785-804 (1993; Zbl 0789.18003)]), predominantly in the catgory \(\underline {\text{Top}}\) of topological spaces. Implicational subcategories of \(\underline {\text{Top}}\) are exactly the intersections of almost reflective subcategories, just as orthogonal subcategories are the intersections of reflective subcategories [cf. \textit{J. Rosický} and the reviewer, Cah. Topologie Géom. Différ. Catégoriques 29, No. 3, 203-215 (1988; Zbl 0669.18001)]. Typical results are: all (Hausdorff, Tikhonov, resp.) spaces form the implicational hull of connected (\(H\)- closed, pseudocompact, resp.) spaces; in the ordered conglomerate of all almost reflective subcategories of \(\underline {\text{Top}}\), binary infima may fail to exist; \(\underline {\text{Top}}\) has no productive almost coreflective subcategory consisting of \(T_ 0\)-spaces only.
reviewed by: Walter Tholen
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 54D35
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 54D80
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 221868
zbMATH Keywords: almost reflective subcategory
zbMATH Keywords: injectivity class
zbMATH Keywords: compact space
zbMATH Keywords: pseudocompact space
zbMATH Keywords: connected space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 221868