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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China (10671173)
文摘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.