Document Type: Original Manuscript
Department of Mathematics, University of Gonabad, P.O. Box 57678-96919, Gonabad, Iran.
Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159- 91775, 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.