Some results on rectifiable spaces

Abstract

In this paper, it is mainly proved that (1) if  $G$ is a rectifiable space, then $In_{l}( G)\leq e(G)$;  (2) if $G$ is a rectifiable space and $A$ is a discrete rectifiable subspace of $G$,  then $|A|\leq l(G)$; (3) every locally compact NSS rectifiable space $G$  is first-countable. The above results  improve the corresponding results in topological groups.