TY - JOUR
AU - Elfard, Ali Sayed
PY - 2015/10/01
Y2 - 2024/04/13
TI - Free paratopological groups
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 16
IS - 2
SE -
DO - 10.4995/agt.2015.1874
UR - https://polipapers.upv.es/index.php/AGT/article/view/1874
SP - 89-98
AB - Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X) is T_0 if X is T_0, we characterize the spaces X for which the group FP(X) is a topological group and then we give a class of spaces $X$ for which the group FP(X) has the inductive limit property.
ER -