Products with a compact factor

✍ Scribed by Michael Starbird

• Publisher: Elsevier Science
• Year: 1976
• Weight: 829 KB
• Volume: 6
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(76)90018-0

✦ Synopsis

In this paper we consider spaces X X Y, where I' is a compact Hausdczff space. Mlast of this paper is devoted to giving mw, simp 'rd proofs to some recent results concerning normality and map extension Iproperties tir !e products. The theorems are of two types. First, we assume that the product X X 1' is ,nal and deduce separation and covering properties for X, for example, that X must 1 v( l?)-collectionwise normal. Second, lu'e assume that X has some special separation p& ~Wies (name&, w(IY;-collectk~nwise normality) and dedr;ce some map eWnsion I -perties for X X Y. For examIJl.e, if A ;md B are closed subsets of X and I{ respectively, ien maps from A X B int0 the real linct R can be extended to all of X X Y regardless of 'lether X X Y is normal or not. The proofs of all the theorems take advanfzge of the natur I one-to-one correspondence between mapsf:XX Y~Wandmsps,':X-*C(Y). r "11 I AMS Subj. Class.: Primary 54C45, S4D15 / I normality in products CNl I collectionwise normal ej rending maps I 1 -._I__-. d ,