fuzzy β-compact relative to X

Last-modified: 2010-06-17 (木) 13:22:00

定義

  • A fuzzy set u in a fuzzy topological space X is said to be fuzzy β-compact relative to X iff for every family μ of [[β -open]]
    fuzzy sets such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cvee_%7bA%5cin%5cmu%7d%20A%5cgeq%20u%28x%29%20%5c%5d%7d%25.png there is a finite subfamily imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5ceta%5csubseteq%5cmu%20%5c%5d%7d%25.png such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5cvee_%7bA%5cin%5ceta%7d%20A%5cgeq%20u%28x%29%20%5c%5d%7d%25.png for every x in S(u), where S(u) is support of a fuzzy set u.

性質

  • Every β-closed? fuzzy subset of a fuzzy β-compact space is fuzzy β-compact relative to X.

出典

  • Hanafy, I.M. Fuzzy β-compactness and fuzzy β-closed spaces (English) Turk. J. Math. 28, No. 3, 281-293 (2004)