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ON GENERALISED METRISABILITY AND CARDINAL INVARIANTS IN QUASITOPOLOGICAL GROUPS

Part of: Peculiar spaces Spaces with richer structures Topological and differentiable algebraic systems Generalities Connections with other structures, applications

Published online by Cambridge University Press:  17 October 2018

ZHONGBAO TANG Open the ORCID record for ZHONGBAO TANG [Opens in a new window]  and
SHOU LIN
ZHONGBAO TANG*
Affiliation:
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, PR China email [email protected]
SHOU LIN
Affiliation:
Institute of Mathematics, Ningde Normal University, Ningde 352100, PR China email [email protected]
*
✉[email protected]
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Abstract

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We consider generalised metrisability and cardinal invariants in quasitopological groups. We construct examples to show that some equalities of cardinal invariants in topological groups cannot be extended to quasitopological groups.

Keywords

cardinal invariantsemimetrisabletopological groupquasitopological group

MSC classification

Primary: 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
Secondary: 22A05: Structure of general topological groups 54E25: Semimetric spaces 54G20: Counterexamples 54H11: Topological groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 302 - 310
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

Supported by the NSFC (Grant Nos.11471153, 11571158, 11801254).

References

Arhangel’skiǐ, A. V., ‘Mappings and spaces’, Russian Math. Surveys 21 (1966), 115–162.Google Scholar
Arhangel’skiǐ, A. V. and Choban, M. M., ‘Examples of quasitopological groups’, Bul. Acad. Ştiinţe Repub. Mold. Mat. 2–3(72–73) (2013), 111–118.Google Scholar
Arhangel’skiǐ, A. V. and Tkachenko, M. G., Topological Groups and Related Structures (Atlantis Press, Amsterdam–Paris, 2008).Google Scholar
Birkhoff, G., ‘A note on topological groups’, Comput. Math. 3 (1936), 427–430.Google Scholar
Engelking, R., General Topology (Heldermann Verlag, Berlin, 1989), revised and completed edition.Google Scholar
Gruenhage, G., ‘Generalized metric spaces’, in: Handbook of Set-Theoretic Topology (eds. Kunen, K. and Vaughan, J. E.) (North-Holland, Amsterdam, 1984), 423–501.Google Scholar
Hodel, R., ‘Cardinal functions I’, in: Handbook of Set-Theoretic Topology (eds. Kunen, K. and Vaughan, J. E.) (North-Holland, Amsterdam, 1984), 1–61.Google Scholar
Kakutani, S., ‘Über die Metrization der Topologischen Gruppen’, Proc. Imp. Acad. (Tokyo) 12 (1936), 82–84.Google Scholar
Li, P. and Mou, L., ‘On quasitopological groups’, Topol. Appl. 161 (2014), 243–247.Google Scholar
Liu, C. and Lin, S., ‘Generalized metric spaces with algebraic structure’, Topol. Appl. 157 (2010), 1966–1974.10.1016/j.topol.2010.04.010Google Scholar
Ravsky, O. V., ‘Paratopological groups I’, Mat. Stud. 16 (2001), 37–48.Google Scholar
Ravsky, O. V., ‘Paratopological groups II’, Mat. Stud. 17 (2002), 93–101.Google Scholar
Shen, R.-X., ‘On generalized metrizable properties in quasitopological groups’, Topol. Appl. 173 (2014), 219–226.Google Scholar
Tang, Z., Lin, S. and Lin, F., ‘A special class of semi(quasi)topological groups and three-space properties’, Topol. Appl. 235 (2018), 92–103.Google Scholar
Tkachenko, M., ‘Paratopological and semitopological groups vs topological groups’, in: Recent Progress in General Topology III (eds. Hart, K. P., van Mill, J. and Simon, P.) (Atlantis Press, Paris, 2014), 825–882.Google Scholar