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On the Problem of Weak Reflections in Compact Spaces
Author(s) -
KOVÁR MARTIN MARIA
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36807.x
Subject(s) - reflection (computer programming) , space (punctuation) , mathematics , locally compact space , pure mathematics , relatively compact subspace , remainder , compact space , characterization (materials science) , physics , computer science , arithmetic , optics , programming language , operating system
In this paper we present, among others, an improvement of Hušek's characterization of the spaces with the weak compact reflection. Our main results are as follows: A topological space has a weak reflection in compact spaces iff the Wallman remainder is finite. If a θ‐regular or T 1 space has a weak compact reflection, then the space is countably compact. A noncompact θ‐regular or T 1 space which is weakly [ω 1 , ∞) r ‐refinable, has no weak reflection in compact spaces.