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Mapping i2 on the free paratopological groups

Fucai Lin Chuan Liu

Abstrak

Let FP(X) be the free paratopological group over a topological space X. For each nonnegative integer n ? N, denote by FPn(X) the subset of FP(X) consisting of all words of reduced length at most n, and in by the natural mapping from (X ? X?1 ? {e})n to FPn(X). We prove that the natural mapping i2:(X ? X?1 d ?{e})2 ? FP2(X) is a closed mapping if and only if every neighborhood U of the diagonal ?1 in Xd x X is a member of the finest quasi-uniformity on X, where X is a T1-space and Xd denotes X when equipped with the discrete topology in place of its given topology.

Penulis (2)

Fucai Lin

Chuan Liu

Format Sitasi

APA MLA BibTeX

Lin, F., Liu, C. (2017). Mapping i2 on the free paratopological groups. https://doi.org/10.2298/pim1715213l

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Informasi Jurnal

Tahun Terbit: 2017
Bahasa: en
Sumber Database: CrossRef
DOI: 10.2298/pim1715213l
Akses: Terbatas