集论拓扑在广义度量理论和覆盖理论的应用

Set theoretic topology is a study direction from mathematical branches of point-set topology, axiomatic set theory, mathematical logic and so on. Centreing on Open Problems in Topology(North-Holland, 1990) edited by J. van Mill and G. M. Reed, this item discusses some related questions about generalized metric theory, covering theory and order topology by new.advances in set theoretic topology. The rich results are obtained containing point-regular structures, sequence-covering mappings, metrizable factorization theorems, g-function methods, properties of meta-compact spaces and normalities of order spaces etc., and some problems posed by topologies A. Arhangel’skii, Y. Tanaka and the others are answered.

点集拓扑学与公理集合论、数理逻辑等分支相互渗透发展起很具活力的研究方向集论拓扑学。集论拓扑学的新发展为解决点集拓扑学中的许多经典问题带来了生机。我们将在已取得的良好工作基础上，应用集论拓扑的最新成就，围绕专著《拓扑学中尚未解决的问题》（英）中所涉及的广义度量理论、覆盖理论以及序拓扑的有关问题，做出有特色、有影响的成果。