Metrizable mapping compactifications

✍ Scribed by George L. Cain Jr.

• Publisher: Elsevier Science
• Year: 1972
• Weight: 695 KB
• Volume: 2
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(72)90011-6

✦ Synopsis

Suppose f:X -+ f(X) = Y is a continuous furaction from one compieteiy regular Hausdorff spar t onto another. There is associated with each possible compactification g of the domain space X a compactification of the mapping f in a unique way; the mapping compactification is called the compactifkation determined by %. e major result of this paper is that if 2 is metrizabie, then th<: domain of the mapping compactification determined bF it is also metrizable if and only if the range Y is. It is also proved that if X1 and X2 are two compactifications of X such that X2 b X1, where 2 is the usual partial order on the collection of all compactifications of X, then tke compactifications off determined by Xr and X2 are related the same way with respect to the usual partial order OR the collection of aii compactika ins of fi 1 AMS Subj. Class.: Primary 54CM: 54C20; Secondary 54E35 1 _ If f:X -+ f(X) = Y 4s a ma ping icon tinums functisn) from pletely regular hkausd orff spa 17~ onto another, a cmzpact$a'c~~i0~i off is a pair (X*,j*) in which X* is a 2iusdorff space conta.inir?g X as a dense pactification of the