摘要
Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits.
Given a compact Hausdorff space X, U(X) denotes the compact Hausdorff space of all the upper semicontinuous functions from X to the unit interval with the dual lim inf topology. Then U is an endofunctor on compact Hausdorff space. It is proved in this note that this functor preserves inverse limits.
基金
TheNSF ( 1 960 1 0 2 6)ofChinaandtheMathematicalCenteroftheMinistryofEducationofChina.
