March 3, 2026Open Access

Notes on the strong Pytkeev property in paratopological groups

Key Points

Sequential spaces arise from a Hausdorff topological space exhibiting the strong pytkeev property, indicating deeper connections in topology.
An affirmative response is given to F.C. Lin, A. Ravsky, and J. Zhang's previous question about k-spaces and the strong pytkeev property.
A regular ?-Fréchet-Urysohn paratopological group demonstrates submetrizability when it has a countable sp-character.
The findings provide partial answers to questions raised by Z.Y. Cai and others about the characteristics of these groups.

Abstract

In this paper, we discuss certain strong Pytkeev property in topological spaces, and prove the following results: (1) a Hausdorff topological space with the strong Pytkeev property is sequential if it is a k-space, which gives an affirmative answer to the question proposed by F.C. Lin, A. Ravsky and J. Zhang 25, Question 4.3; (2) a regular ?-Fr?chet-Urysohn paratopological group with countable sp-character is submetrizable, and if it still has the property (?), then it is first-countable, which gives a partial answer to the question proposed by Z.Y. Cai, P.Q. Ye, S. Lin and B. Zhao 7, Question 2.8.

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