In this paper, we give some properties of rectifiable spaces and their relationship with P-space, metrizable space. These results are used to generalize some results in [2], [9] and [12]. Moreover, we give the conditions for a rectifiable space to be second-countable.
We introduce the notion of an L-Ponomarev system (f, M, X, P * n), and give characterizations of certain msss-images (resp., mssc-images) of locally separable metric spaces. As an application, we get a new characterization of quotient msss-images (mssc-images) of locally separable metric spaces, which is helpful in solving Velichko's question (1987). Recently, Dung gave some characterizations for certain msss-images (resp., mssc-images) of locally separable metric spaces in the class of regular and T 1-spaces (see in [3, 4]). This leads us to consider the following question.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.