Metrizable compactification of ω is unique

✍ Scribed by Jun Terasawa

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 131 KB
• Volume: 76
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(96)00114-9

✦ Synopsis

For every compact metrizable space X there is a melrizable compactification/J(X) of w whose remainder/~(X) \ w is homeomorphic to X. And this p(X) is unique up to homeomorphisms leaving every point of X fixed. Also/t has a functorial property in the sense that every continuous map X ---r Y can be extended (not uniquely) to a continuous map ~u(X) ---> p(Y): and if the former is surjeclive so can be the latter. As an application, a simple argume,',t is provided for the fact that the Cantor set is the universal space for the class of all zero-dimensional compact metrizable spaces.