取值于序拓扑向量空间的映射与层空间

Maps to Ordered Topological Vector Spaces and Stratifiable Spaces

中文关键词:  层空间  $k$-半层空间  取值于序拓扑向量空间的映射  下(上)半连续性

英文关键词:stratifiable spaces  $k$-semi-stratifiable spaces  maps to ordered topological vector spaces  lower (upper) semi-continuity

中文摘要:

      在文[Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169}(3): 51--70]中, Yamazaki开始了对取值于序拓扑向量空间的映射的研究,利用取值于序拓扑向量空间的映射给出了对单调可数仿紧空间及其它一些空间类的等价刻画.本文中,应用Yamazaki的方法,我们利用取值于序拓扑向量空间的映射给出对层空间及$k$-半层空间的若干等价刻画.

英文摘要:

      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.