*Definition [#kabbb56a]
Let V be the subset family of a topological space X. A finite sequence &ref(http://www.eaflux.com/imgtex/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 &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$W_%7bi%7d%5ccap%20W_%7bi+1%7d%5cneq%20%5cemptyset$%7d%25.png); for every &ref(http://www.eaflux.com/imgtex/imgtex.fcgi?%5bres=100%5d%7b$1%5cle%20i%5cle%20s-1$%7d%25.png);. The family &ref(http://www.eaflux.com/imgtex/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 [#m71e2ce9]
D. Buhagiar and T. Miwa, ''On superparacompact and Lindeloef GO-spaces'', Houston J. Math. Vol.24, No.3, 1998.