More on remainders close to metrizable spaces
TLDR
Henriksen and Isbell as mentioned in this paper showed that if a compact Hausdorff space X is first countable at least at one point, and X can be represented as the union of two complementary dense subspaces Y and Z, each of which is homeomorphic to a topological group (not necessarily the same), then X is separable and metrizable.About:
This article is published in Topology and its Applications.The article was published on 2007-03-15 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Metrization theorem & Topological manifold.read more
Citations
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Two types of remainders of topological groups
TL;DR: Arhangel'skii et al. as discussed by the authors proved a Dichotomy Theorem: for each Hausdorff compactification bG of an arbitrary topological group G, the remainder bG\G is either pseudocompact or Lin- delof.
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On rectifiable spaces and paratopological groups
Fucai Lin,Rongxin Shen +1 more
TL;DR: In this paper, Liu et al. discuss 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, then AB is ωnarrow in G, which gives an affirmative answer for A.V. Arhangel'shii and M. Tkachenko (2008) [7, Open problem 5.1] ; (2) every bisequential or weakly first-countable rectifiable space is met
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Remainders of rectifiable spaces
TL;DR: In this article, the Dichotomy Theorem for rectifiable spaces is generalized to the case of topological groups, and it is shown that for any Hausdorff compactification bG of an arbitrary rectifiable space G the remainder bG ∖ G is either pseudocompact or Lindelof.
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A note on rectifiable spaces
Fucai Lin,Chuan Liu,Shou Lin +2 more
TL;DR: Arhangel et al. as discussed by the authors showed that a rectifiable space X is strongly Frechet-Urysohn if and only if X is an α 4 -sequential space.
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Generalized metric spaces with algebraic structures
Chuan Liu,Shou Lin +1 more
TL;DR: In this paper, it was shown that a first-countable paratopological group which is a β -space is developable, and a Hausdorff, separable, non-metrizable topological group is also developable.
References
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Book
Handbook of Set-Theoretic Topology
TL;DR: In this article, the authors introduce the notion of cardinal functions and the proper forcing axiom for counting S and L spaces, and present a theory of nonmetrizable manifolds.
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Generalized Metric Spaces
TL;DR: The notion of generalized metric spaces as mentioned in this paper is a generalization of metric spaces that is closely related to what is known as metrization theory and can be used to characterize the images or pre-images of the metric spaces under certain kinds of mappings.
Book
Uniform Structures on Topological Groups and Their Quotients
Walter Roelcke,Susanne Dierolf +1 more
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Remainders in compactifications and generalized metrizability properties
TL;DR: Husek and van Mill as mentioned in this paper showed that if a non-locally compact topological group G is metrizable at infinity, then G is a Lindelof p-space, and the Souslin number of G is countable.