广义度量空间问题成立的可能性

The Possibility of the Problem on Generalized Metric Space

摘要: 本文尝试证明广义度量空间问题中层空间等价的问题。通过研究可度量空间中有关有限基和正则性的定义和性质，得到了具有 局部有限基的正则空间，再通过Nagata-Smirnov度量化定理将 局部有限基弱化为闭包保持基就得到了关于构造层空间的方法，这里利用构造拓扑空间和建立连续映射的方法，证明了所构造空间M1与M3等价，从而解决了广义度量空间中所构造的三种层空间相互等价的问题。

Abstract: This paper tries to prove the equivalence of stratifiable spaces in the problem on generalized metric space. The definitions and properties of finite basis and regularity in metric space are studied. The regular space with   local finite basis is obtained. In addition, the method of building space is obtained by using the Nagata-Smirnov Metrization Theorem to weaken the   local finite basis to the closure keep basis. A method of constructing a topological space and establishing a continuous mapping is used here. The space M1 is equal to the space M3. In this way, three kinds of spatial equivalent problems in generalized metric space are solved.