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- W1905583718 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.
- W1905583718 created "2016-06-24" @default.
- W1905583718 creator A5088391450 @default.
- W1905583718 date "2015-10-01" @default.
- W1905583718 modified "2023-09-29" @default.
- W1905583718 title "Free paratopological groups" @default.
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- W1905583718 doi "https://doi.org/10.4995/agt.2015.1874" @default.
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