摘要
Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα ： X → Xα is an open and onto map and X is A-paracompact. We prove that if each Xα is B（LF, ω^2）-refinable （hereditarily B（LF, ω^2）- refinable）, then X is B（LF, ω^2）-refinable （hereditarily B（LF,ω ^2）-refinable）. Furthermore, we show that B（LF, ω^2）-refinable spaces can be preserved inversely undcr closed maps.
Let X be the limit of an inverse system {Xα, παβ, ∧} and and let λ be the cardinal number of A. Assume that each projection πα ： X → Xα is an open and onto map and X is A-paracompact. We prove that if each Xα is B（LF, ω^2）-refinable （hereditarily B（LF, ω^2）- refinable）, then X is B（LF, ω^2）-refinable （hereditarily B（LF,ω ^2）-refinable）. Furthermore, we show that B（LF, ω^2）-refinable spaces can be preserved inversely undcr closed maps.
基金
Supported by the National Natural Science Foundation of China (10671173)
