Author: Zhao Dongsheng, Mathematics and Mathematics Education, National Institute of Education Singapore, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616(firstname.lastname@example.org).
A partial order on the set of continuous endomappings, pp. 311-326.
ABSTRACT. Motivated by the reflexive operator algebra problem, we introduce a new partial order on the set EndC(X) of all continuous endomappings on a topological space X. We study the relationship between the topological structure and the order structure, and we establish conditions for certain families of continuous endomappings to be reflexive. We introduce the V-regular spaces and show that if X and Y are V-regular spaces, then the two semigroups EndC(X) and EndC(Y) are isomorphic if and only if X and Y$ are homeomorphic.