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Volume 36 • Number 4 • 2013 |
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Metrizability of Rectifiable Spaces
Fucai Lin
Abstract.
A topological space G is said to be a {\it rectifiable space} provided that there are a surjective homeomorphism φ:G×G→G×G and an element e∈G such that π1∘φ=π1 and for every x∈G we have φ(x,x)=(x,e), where π1:G×G→G is the projection to the first coordinate. In this paper, we firstly show that every submaximal rectifiable space G either has a regular Gδ-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 α4-rectifiable space determined by a point-countable cover G consisting of bisequential subspaces then it is metrizable, which generalizes a result of Lin and Shen's.
2010 Mathematics Subject Classification:54A25, 54B05, 54E20, 54E35
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