Cross-complementary subsets in paratopological groups

Temel Bulgular & Veri:Tkachenko [Topological Groups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about the above question in paratopological groups [Open problem 4.6.9, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008].

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Sonuç & Katkı:Arhangel’skii's results hold for $k$-gentle paratopological groups.

🔬Tür:Araştırma Makalesi

📍Kapsam:2003 Verileri

⚙️Değişkenler:metrizable groups · paratopological groups · $k$-gentle paratopological groups

Abstract

The following general question is considered by A.V. Arhangel’skii [Perfect mappings in topological groups, cross-complementary subsets and quotients, Comment. Math. Univ. Carolin. 2003]. Suppose that $G$ is a topological group, and $F , M$ are subspaces of $G$ such that $G = MF$. Under these general assumptions, how are the properties of $F$ and $M$ related to the properties of $G$? Also, A.V. Arhangel’skii and M. Tkachenko [Topological Groups and Related Structures, Atlantis Press, World Sci., 2008] asked what is about the above question in paratopological groups [Open problem 4.6.9, Topological Groups and Related Structures, Atlantis Press, World Sci. 2008]. In this paper, we mainly consider this question and some positive answers to this question are given. In particular, we find many A.V. Arhangel’skii's results hold for $k$-gentle paratopological groups.

Anahtar kelimeler

metrizable groups paratopological groups $k$-gentle paratopological groups perfect mappings paracompact $p$-spaces countable tightnesses

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Bu Makaleye Atıf Yap

LİN, W., FANG, L., XİE, L. (2020). Cross-complementary subsets in paratopological groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 1–7. https://ajindex.com/articles/669289

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Kaynakça (11)

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