M. Kowkabi - Department of Mathematics, University of Gonabad, P.O. Box ۵۷۶۷۸-۹۶۹۱۹, Gonabad, Iran.
B. Mashayekhi - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.
H. Torabi - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box ۱۱۵۹- ۹۱۷۷۵, Mashhad, Iran.

In this paper, by reviewing the concept of subcovering and semicovering maps, we extend the notion of subcovering map to subsemicovering map. We present some necessary or sufficient conditions for a local homeomorphism to be a subsemicovering map. Moreover, we investigate the relationship between these conditions by some examples. Finally, we give a necessary and sufficient condition for a subsemicovering map to be semicovering.

local homeomorphism, fundamental group, covering map, semicovering map subcovering map, subsemicovering map