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thick compact

Last-modified: 2011-03-24 (木) 22:40:38

Definition Edit

A Hausdorff space is called a thick compact space if for each cardinality m, there exist dense subsets X_m such that: if imgtex.fcgi?%5bres=100%5d%7b$M%5csubset%20X_m$%7d%25.png and imgtex.fcgi?%5bres=100%5d%7b$%7cM%7c%5cle%20m$%7d%25.png, then imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bcl%7dM%5csubset%20X_m$%7d%25.png and imgtex.fcgi?%5bres=100%5d%7b$%5cmathrm%7bwcl%7dM%5cle%20m$%7d%25.png
where wclM denotes the weight of clM.

Reference Edit

Marian Turzanski, Strong sequences, binary families and Esenin-Volpin's theorem, Comment. Math. Univ. Carolin. 33, 3 (1992) 563-569