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This content will become publicly available on June 20, 2026

Title: Relative cell complexes in closure spaces
Abstract We give necessary and sufficient conditions for certain pushouts of topological spaces in the category of Čech’s closure spaces to agree with their pushout in the category of topological spaces. We prove that in these two categories, the constructions of cell complexes by a finite sequence of closed cell attachments, which attach arbitrarily many cells at a time, agree. Likewise, the constructions of CW complexes relative to a compactly generated weak Hausdorff space that attach only finitely many cells, also agree. On the other hand, we give examples showing that the constructions of finite-dimensional CW complexes, CW complexes of finite type, and relative CW complexes that attach only finitely many cells, need not agree.  more » « less
Award ID(s):
2324353
PAR ID:
10623995
Author(s) / Creator(s):
Publisher / Repository:
Canadian Mathematical Society
Date Published:
Journal Name:
Canadian Mathematical Bulletin
ISSN:
0008-4395
Page Range / eLocation ID:
1 to 9
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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