Bulletin of the Belgian Mathematical Society - Simon Stevin

Topological monomorphisms between free paratopological groups

Fucai Lin

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Abstract

Suppose that $X$ is a subspace of a Tychonoff space $Y$. Then the embedding mapping $e_{X, Y}: X\rightarrow Y$ can be extended to a continuous monomorphism $\hat{e}_{X, Y}: AP(X)\rightarrow AP(Y)$, where $AP(X)$ and $AP(Y)$ are the free Abelian paratopological groups over $X$ and $Y$, respectively. In this paper, we mainly discuss when $\hat{e}_{X, Y}$ is a topological monomorphism, that is, when $\hat{e}_{X, Y}$ is a topological embedding of $AP(X)$ to $AP(Y)$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 3 (2012), 507-521.

Dates
First available in Project Euclid: 14 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1347642379

Digital Object Identifier
doi:10.36045/bbms/1347642379

Mathematical Reviews number (MathSciNet)
MR3027357

Zentralblatt MATH identifier
1259.54005

Subjects
Primary: 54C20: Extension of maps 54C25: Embedding 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54E15: Uniform structures and generalizations 54H11: Topological groups [See also 22A05]

Keywords
Free paratopological groups topological monomorphism free topological groups quasi-uniform quasi-P$^{\ast}$-embedded quasi-P-embedded quasi-pseudometric universal quasi-uniformity

Citation

Lin, Fucai. Topological monomorphisms between free paratopological groups. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 3, 507--521. doi:10.36045/bbms/1347642379. https://projecteuclid.org/euclid.bbms/1347642379


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