On rectifiable spaces and paratopological groups

By Fucai Lin, R. Shen. 2011

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Abstract We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If A and B are ω-narrow subsets of a paratopological group G, then AB is ω-narrow in G, which gives an affirmative answer for A.V. Arhangel'shii and M. Tkachenko (2008) [7, Open problem 5.1.9] ; (2) Every bisequential or weakly first-countable rectifiable space is metrizable; (3) The properties of Frechet–Urysohn and strongly Frechet–Urysohn coincide in rectifiable spaces; (4) Every rectifiable space G contains a (closed) copy of S ω if and only if G has a (closed) copy of S 2 ; (5) If a rectifiable space G has a σ-point-discrete k-network, then G contains no closed copy of S ω 1 ; (6) If a rectifiable space G is pointwise canonically weakly pseudocompact, then G is a Moscow space. Also, we consider the remainders of paratopological groups or rectifiable spaces, and answer two questions posed by C. Liu (2009) in [20] and C. Liu, S. Lin (2010) in [21] , respectively.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6cbdd4ae174784740c8db3c9e3d9efb24034562b