ON SEMICOVERING, SUBSEMICOVERING, AND SUBCOVERING MAPS

Abstract

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.

Keywords

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