k-semistratifiable spaces and expansions of set-valued mappings

Abstract

In this paper, the concept of k-upper semi-continuous set-valued mappings is introduced. Using this concept, we give characterizations of k-semistratifiable and k-MCM spaces, which answers a question posed by Xie and Yan.

Keywords

• locally bounded set-valued mappings
• k-MCM spaces
• k-semistratifiable spaces
• lower semi-continuous (l.s.c.)
• k-upper semi-continuous (k-u.s.c.)