Open Access
Translator Disclaimer
september 2012 Topological monomorphisms between free paratopological groups
Fucai Lin
Bull. Belg. Math. Soc. Simon Stevin 19(3): 507-521 (september 2012). DOI: 10.36045/bbms/1347642379

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 $AP(Y)$.

Citation

Download Citation

Fucai Lin. "Topological monomorphisms between free paratopological groups." Bull. Belg. Math. Soc. Simon Stevin 19 (3) 507 - 521, september 2012. https://doi.org/10.36045/bbms/1347642379

Information

Published: september 2012
First available in Project Euclid: 14 September 2012

zbMATH: 1259.54005
MathSciNet: MR3027357
Digital Object Identifier: 10.36045/bbms/1347642379

Subjects:
Primary: 54C20 , 54C25 , 54D35 , 54E15 , 54H11

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

Rights: Copyright © 2012 The Belgian Mathematical Society

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.19 • No. 3 • september 2012
Back to Top