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- W2109638186 abstract "The result often known as Joiner's lemma is fundamental in understanding the topology of the free topological group $F(X)$ on a Tychonoff space$X$. In this paper, an analogue of Joiner's lemma for the free paratopological group $FP(X)$ on a $T_1$ space $X$ is proved. Using this, it is shown that the following conditions are equivalent for a space $X$: (1) $X$ is $T_1$; (2) $FP(X)$ is $T_1$; (3) the subspace $X$ of $FP(X)$ is closed; (4) the subspace $X^{-1}$ of $FP(X)$ is discrete; (5) the subspace $X^{-1}$ is $T_1$; (6) the subspace $X^{-1}$ is closed; and (7) the subspace $FP_n(X)$ is closed for all $n in N$, where $FP_n(X)$ denotes the subspace of $FP(X)$ consisting of all words of length at most $n$." @default.
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- W2109638186 date "2012-04-06" @default.
- W2109638186 modified "2023-10-02" @default.
- W2109638186 title "On the topology of free paratopological groups" @default.
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- W2109638186 doi "https://doi.org/10.1112/blms/bds031" @default.
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