商空间X/M中的遗传性

On the Genetic Character of Quotient Space X/M

讨论了商空间X／M中的遗传性,得到了如下结论:[1]定理1:设X是Banach空间,M是X的可逼近的闭子空间,则如果X是CLωR空间■商空间X／M是CLωR空间。[2]定理2:设X是Banach空间,M是X的可逼近的闭子空间,则如果X是CLKR(ω-严格凸,K-严格凸,WLωR,WLKR,LωR,LKR)空间,那么商空间X／M是CLKR(ω-严格凸,K-严格凸,WLω R,WLKR,Lω,LKR)空间。[3]对M是闭子空间,讨论了ωR,KR,Wω R,WKR相应的遗传性。

The genetic character of the quotient space X/M is discussed and the following conclusions are given. [ 1 ] Theorem 1 ： Suppose X be the Banach space and M the approximatable close subspace by X, then if X is CLωR space → quotient space X/M is CLωR space. [2] Theorem 2： Suppose X be the Banach space and M the appreximatable close subspace by X, then if X is CLKR（ to -strict convexity, K- strict convexity, WLωR, WLKR, LωR, LKR） space, the quotient X/M is CLKR（ω-strict convexity, K - strict convexity, WLωR, WLKR, LωR, LKR） space. [3] If M is close subspace, the corespondent genetic character of ωR, KR, WωR, WKR is discussed.