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- W4300553601 abstract "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." @default.
- W4300553601 created "2022-10-03" @default.
- W4300553601 creator A5088391450 @default.
- W4300553601 date "2012-12-22" @default.
- W4300553601 modified "2023-10-15" @default.
- W4300553601 title "Free paratopological groups" @default.
- W4300553601 doi "https://doi.org/10.48550/arxiv.1212.5749" @default.
- W4300553601 hasPublicationYear "2012" @default.
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