Some Supra Covering Properties On Supra Topological Spaces

This paper gives the definitions of supra countably compact,supra ?-countable compactness and supra b-countable compactness in supra topological space,and studies several supra topological spaces properties,including properties of its subspace and the mapping on it.This paper is divided into four chapters.In the first chapter,we mainly introduce some basic definitions and basic theorems of the supra topological space.In the second chapter,equivalent conditions of supra countably compact space are given,some properties of supra countably compact space are studied,including the relationship between supra countably compact space and some special supra topological space,and the nature of supra closed subspaces.The third chapter introduces the concept of supra ?-countably compact space,almost supra ?-countably compact space and weak supra ?-countably compact space,gives the relationship between some topological spaces and studies their properties.In the fourth chapter,supra b-countably compact space are introduced and the basic properties of supra subspaces of supra b-countable compactness are studied.The main results are as follows:1.The supra closed subspace of a supra countably compact space is supra countably compact space.2.A supra T2 space is supra compact space if and only if X is a supra countably compact space with supra lindelof property.3.Let X is a supra countably compact space and Y is a supra T2 space.There exists a S~*continuous surjectionf from X onto Y,then Y it is a supra countably compact space.4.The supra closed subspace of supra ?-countably compact space is a supra countably compact space.5.The image of a supra ?-countably compact space(almost supra ?-countably compact space)under a supra ?-continuity is supra countably compact(almost supra countably compact).6.The supra b-closed subset of a supra b-countably compact space is a supra countable compactness.