k-semistratifiable spaces and expansions of set-valued mappings

Peng-Fei Yan, Xing-Yu Hu, Li-Hong Xie


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.


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.)

Subject classification

54C65; 54C60.

Full Text:



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