In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T_(0) enriched closure spaces.More precisely,we define and study Enr-convergence in T_(0) enriched closure spaces.Especi...In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T_(0) enriched closure spaces.More precisely,we define and study Enr-convergence in T_(0) enriched closure spaces.Especially,we give a sufficient and necessary condition for Enr-convergence in T_(0) enriched closure spaces to be topological.展开更多
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 o...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11531009,12101383)the Fundamental Research Funds for the Central Universities(Grant No.GK202103006)。
文摘In this paper,we give a novel framework for lim-inf convergence in posets through the concept of T_(0) enriched closure spaces.More precisely,we define and study Enr-convergence in T_(0) enriched closure spaces.Especially,we give a sufficient and necessary condition for Enr-convergence in T_(0) enriched closure spaces to be topological.
文摘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.
