A unified theory for homotopy principles for multimaps

Abstract

In this article, we present a definition of d-essential and d–L-essential maps in completely regular topological spaces and we establish a homotopy property for both d-essential and d–L-essential maps. Also using the notion of extendability, we present new continuation theorems.

Keywords:

• continuation methods
• d-essential
• fixed points

AMS Subject Classifications::

• 47H10
• 47J05