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monotonically orthocompact

Last-modified: 2011-08-08 (月) 22:23:13

Definition Edit

  • A topological space X is called monotonically orthocompact provided that there is an operator T: E →S from the set E of all open covers of X to the set S of all transitive neighbornets of X such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20T%28%7bC%7d%29%5csubseteq%20T%28%7bD%7d%29%20%5c%5d%7d%25.png whenever imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20C%2cD%20%5cin%20E%20%5c%5d%7d%25.png and C is a refinement of D , and such that imgtex.fcgi?%5bres=100%5d%7b%5c%5b%20%5c%7bT%28C%29%28x%29%20%7c%5c%20x%20%5cin%20X%5c%7d%20%5c%5d%7d%25.png refines ff whenever C in E

Reference Edit

  • Junnila, Heikki J.K. and Künzi, Hans-Peter A., Ortho-bases and monotonic properties.,[J] Proc. Am. Math. Soc. 119, No.4, 1335-1345 (1993).