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λ-compact

Last-modified: 2010-12-28 (火) 22:08:08

Definition Edit

Let X be a Tychonoff space, υX the Hewitt-Nachbin realcompactification.
For subset A of X, we write imgtex.fcgi?%5bres=100%5d%7b$Z%28f%29=f%5e%7b-1%7d%28%5c%7b0%5c%7d%29$%7d%25.png, imgtex.fcgi?%5bres=100%5d%7b$M%5eA=%5c%7b%20f%5cin%20C%28X%29:A%5csubset%5cmathrm%7bcl%7d_%7b%5cbeta%20X%7dZ%28f%29%20%5c%7d$%7d%25.png, imgtex.fcgi?%5bres=100%5d%7b$O%5eA=%5c%7b%20f%5cin%20C%28X%29:A%5csubset%20%5cmathrm%7bint%7d_%7b%5cbeta%20X%7d%5cmathrm%7bcl%7d_%7b%5cbeta%20X%7dZ%28f%29%20%5c%7d$%7d%25.png.
We say X is λ-compact iff imgtex.fcgi?%5bres=100%5d%7b$M%5e%7b%5cupsilon%20X-X%7d=O%5e%7b%5cupsilon%20X-X%7d$%7d%25.png.

Remark Edit

Reference Edit

  • I.Blum and S.Swaminathan, A note on intersections of ideals in rings of continuous functions, in "Topology", Coloquia Mathematica Societatis Janos Bolyai 23 Vol I, North Holland, Amsterdam, 1980, pp.155-162.
  • http://www.utm.edu/staff/jschomme/weakdefs.html