Metrizability of Rectifiable Spaces

Fucai Lin

Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 4

Résumé

A topological space $G$ is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism $\varphi :G\times G\rightarrow G\times G$ and an element $e\in G$ such that $\pi_{1}\circ \varphi =\pi_{1}$ and for every $x\in G$ we have $\varphi (x, x)=(x, e)$, where $\pi_{1}: G\times G\rightarrow G$ is the projection to the first coordinate. In this paper, we firstly show that every submaximal rectifiable space $G$ either has a regular $G_{\delta}$-diagonal, or is a $P$-space. Then, we mainly discuss rectifiable spaces are determined by a point-countable cover, and show that if $G$ is an $\alpha_{4}$-rectifiable space determined by a point-countable cover $\mathscr{G}$ consisting of bisequential subspaces then it is metrizable, which generalizes a result of Lin and Shen's.

Détail

Classification : 54A25, 54B05, 54E20, 54E35