Paper Info
Title
An elementary approach to ‘Algebra ∩ topology = compactness’
Abstract
Herrlich and Strecker characterized the category Comp2 of compact Hausdorff spaces as the only nontrivial full epireflective subcategory in the category Top2 of all Hausdorff spaces that is concretely isomorphic to a variety in the sense of universal algebra including infinitary operations. The original proof of this result requires Noble's theorem, i.e. a space is compact Hausdorff iff every of its powers is normal, which is far from being elementary. Likewise, Petz' characterization of the class of compact Hausdorff spaces as the only nontrivial epireflective subcategory of Top2, which is closed under dense extensions (= epimorphisms in Top2) and strictly contained in Top2 is based on a result by Katetov stating that a space is compact Hausdorff iff its every closed subspace is H-closed. This note offers an elementary approach for both, instead.
Year
DOI
Venue
1996
10.1007/BF00122689
Applied Categorical Structures
Keywords
DocType
Volume
18B30,18C05,54B30,54D30,Reflective subcategories of,Top,varietal functors,compactness
Journal
4
Issue
ISSN
Citations 
4
1572-9095
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
G. Richter100.34