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finite component cover

Last-modified: 2010-09-01 (水) 21:44:47

Definition Edit

Let V be the subset family of a topological space X. A finite sequence imgtex.fcgi?%5bres=100%5d%7b$%5c%7bW_1%2c%5ccdots%2cW_s%5c%7d%5csubset%20%5cmathcal%7bV%7d$%7d%25.png is called a chain iff imgtex.fcgi?%5bres=100%5d%7b$W_%7bi%7d%5ccap%20W_%7bi+1%7d%5cneq%20%5cemptyset$%7d%25.png for every imgtex.fcgi?%5bres=100%5d%7b$1%5cle%20i%5cle%20s-1$%7d%25.png. The family imgtex.fcgi?%5bres=100%5d%7b$%5cmathcal%7bV%7d$%7d%25.png is called connected iff for every W, U in V, there is a chain from W to U. A maximal connected subfamily of V is called component. A star-finite open cover of X is called finite componet cover iff the number of elements of each component is finite.

Reference Edit

D. Buhagiar and T. Miwa, On superparacompact and Lindeloef GO-spaces, Houston J. Math. Vol.24, No.3, 1998.