Maps to Ordered Topological Vector Spaces and Stratifiable Spaces

Abstract:

      In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51--70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and $k$-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.