Countable networks on Malykhin's maximal topological group
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Márquez, Edgar [1]
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[1] Universidad Autónoma Metropolitana
Universidad Autónoma Metropolitana
México
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- Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 2, 2023, págs. 239-246
- Idioma: inglés
- DOI: 10.4995/agt.2023.18517
- Enlaces
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Resumen
We present a solution to the following problem: Does every countable and non-discrete topological (Abelian) group have a countable network with infinite elements? In fact, we show that no maximal topological space allows for a countable network with infinite elements. As a result, we answer the question in the negative. The article also focuses on Malykhin's maximal topological group constructed in 1975 and establishes some unusual properties of countable networks on this special group G. We show, in particular, that for every countable network N for G, the family of finite elements of N is also a network for G.
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Referencias bibliográficas
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- E. K. van Douwen, The Integers and Topology, in: Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, Eds.), Elsevier Science Publ....
- D. H. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, Cambridge, 1984. https://doi.org/10.1017/CBO9780511896972
- E. Márquez and M. Tkachenko, D-independent topological groups, Topology Appl. 300 (2021), 107761. https://doi.org/10.1016/j.topol.2021.107761
