A note on the remainders of rectifiable spaces

In this paper‎, ‎we mainly investigate how the generalized metrizability properties of the remainders affect the metrizability of rectifiable spaces‎, ‎and how the character of the remainders affects the character‎ ‎and the size of a rectifiable space‎. ‎Some results in [A. V‎. ‎Arhangelʹski\v{\i} and J‎. ‎Van Mill‎, ‎On topological groups with a first-countable remainder‎, ‎{\em Topology Proc.} {42} (2013) ‎157--163‎.] and [F. C‎. ‎Lin‎, ‎C‎. ‎Liu‎, ‎S‎. ‎Lin‎, ‎A note on rectifiable spaces‎, ‎{\em Topology Appl.} {159} (2012)‎, ‎no‎. ‎8‎, ‎2090--2101‎.] are improved‎, ‎respectively‎.