摘要
在一般拓扑学中有大量的广义度量空间,如Nagata-空间,k-半分层空间,σ-空间和半分层空间等,它们之间的关系已经明确。wN-空间,kβ-空间,wσ-空间和β-空间分别是Nagata-空间,k-半分层空间,σ-空间和半分层空间的自然推广,它们在广义度量空间之间的关系和度量化定理中起着重要的作用,但是它们之间的关系并不明确。文章探讨了它们的关系,结果表明:wN-空间■kβ-空间,弱子序列kβ-空间■wσ-空间并且wσ-空间■β-空间,其逆一般不成立。
There exists a large quantity of generalized metric spaces in general topology, for example, Nagata-spaces, k-semi-stratifiable spaces, σ-spaces and semi-stratifiable spaces and so on, and the relationships among them are definitely known, wN- spaces, kβ-spaces, wσ-spaces and β-spaces were introduced respectively as the generalizations of Nagata-spaces, k-semi-stratifiable spaces, σ- spaces and semi-stratifiable spaces. They play important roles in the relationships among generalized metric spaces and metrizable theorems, but the relationships among them are not known. In this paper, the relationships among them are discussed, and the following results are obtained： ωN -spaces → kβ - spaces,weak subsequence kβ-spaces →ωσ-spaces and ωσ-spaces →β-spaces, but the inverse implications are not true.
出处
《山东建筑大学学报》
2011年第5期433-435,共3页
Journal of Shandong Jianzhu University
基金
山东省高等学校教学研究项目(2009262)
