q-紧空间的进一步探讨及推广

The Further Exploration and Promotion of the q-Compact Space

引入了q-基,q-闭映射,q-完备映射,q-邻域等概念,对其性质作了初步地探讨,分别给出了q-闭映射,q-基的充要条件。在此基础上,对q-紧空间的性质作了进一步地探讨,并对q-紧空间作了局部化的推广,得到了一些较好的结果。主要结果有:q-不定映射保持q-紧性,q-不定的q-开映射保持局部q-紧性,局部q-紧空间在q-完备映射下的像是局部q-紧空间等.所得的结果丰富了点集拓扑学的基础理论知识。

The concepts of q-base,q-closed mapping,q-perfect mapping,concepts q-neighborhood were introduced,and its properties were studied in a preliminary way.Besides necessary and sufficient condition of q-closed mapping,q-based were given.On this basis,on the nature of q-compact spaces are further explored,and make a partial q-compact space-based promotion,and it gets some good results.The main results showed：q-irresolute mapping maintains q-compactness,q-continuous and q-open mapping uncertain keeps the local q-compact,local q-compact space in the q-perfect mapping such as under the local q-compact space.The results enriched the basic theoretical knowledge of the point set topology.