Metrizability of rectifiable spaces

A topological space G is said to be a rectifiable space provided that there are a surjective homeomorphism ? : G x G?G x G and an element e ? G such that ?1? ? = ?1 and for every x ? G we have ?(x,x) = (x,e), where ?1 : G x 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 G?-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 ?4-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.