Countable networks on Malykhin's maximal topological group




countable network, resolvable, linear, P-point, P-space


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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Author Biography

Edgar Márquez, Universidad Autónoma Metropolitana

Departamento de Matemáticas


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D. H. Fremlin, Consequences of Martin's Axiom, Cambridge University Press, Cambridge, 1984.

E. Márquez and M. Tkachenko, D-independent topological groups, Topology Appl. 300 (2021), 107761.




How to Cite

E. Márquez, “Countable networks on Malykhin’s maximal topological group”, Appl. Gen. Topol., vol. 24, no. 2, pp. 239–246, Oct. 2023.



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