Σ-subset

Last-modified: 2010-05-27 (木) 13:41:11

定義

  • If Γ is a set, we put imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cSigma%28%5cGamma%29=%5c%7bx%20%5cin%20%5cmathbb%7bR%7d%5e%7b%5cGamma%7d%5cmid%20%5c%7b%5cgamma%20%5cin%20%5cGamma%20%5cmid%20x%28%5cgamma%29%20%5cneq%200%5c%7d%5ctext%7b%20is%20countable%7d%5c%7d%20%5c%5d%7d%25.png .
  • We say that A \subset K is a Σ-subset of K if there is a homeomorphic injection h of K into some imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cmathbb%7bR%7d%5e%7b%5cGamma%7d%20%5ctext%7b%20such%20that%20%7d%20A=h%5e%7b-1%7d%5cbigl%28h%28K%29%20%5ccap%20%5cSigma%28%5cGamma%29%5cbigr%29.%20%5c%5d%7d%25.png .

出典

Kalenda, Ondřej(CZ-KARLMP-MA),A characterization of Valdivia compact spaces, (English summary)Collect. Math. 51 (2000), no. 1, 59--81.