第一可数空间

一类g-第一可数空间的刻画

Characterizations of Certain g - first Countable Spaces

引进了1-序列商映射，证明了1-序列商映射象保持sn-第一可数空间。

In this paper , we introduce 1-sequentially quotient mappings , and prove that 1-sequentially quotient mappings preserve sn-first countable spaces .

g-第一可数空间和g-度量空间有许多特殊的拓扑性质，研究它们在映射下的不变性是非常必要的。

G-first countable spaces and g-metri / able spaces have many important topological properities so to investigate which mapping preserves them is very necessary .

然而后来的拓扑学家主要在广义度量空间内研究具有某些点可数性质弱基的空间，比如g-第一可数空间，g-第二可数空间，g-可度量空间等。

But these topology scholars mainly paid their attentions to generalized metric spaces which have point countable weak bases , such as g-first countable , g-second countable , g-metrizable etc.

第三节研究了文献[5]中的一个例子，证明了完备映射不保持g-第一可数空间，g-度量空间，sn-第一可数空间，sn-度量空间。

In the third section , we investigate an example to show that perfect mappings do not preserve g-first countable spaces , g-metrizable spaces , sn-first countable spaces and sn-metrizable spaces .

本文在第二节研究了弱开映射与序列商映射，几乎开映射的关系，证明了有限到一的弱开映射保持g-第一可数空间；弱开闭映射保持g-度量空间。

In the second section of this article , we investigate weak open mappings have the relations with other mappings and prove that the finite-to-one weak open mappings preserve g-first countable , spaces and weak open closed mapping preserve g-metrizable spaces .

第一可数性公理空间的性质

The Property of First Countable Spaces