A theorem on remainders of topological groups
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DOI: 10.1016/j.topol.2017.02.003
Abstract: It has been established in [7–9] that a non-locally compact topological group G with a first-countable remainder can fail to be metrizable. On the other hand, it was shown in [6] that if some remainder… read more here.
Keywords: remainder; theorem remainders; topological groups; topology ... See more keywords
On strongly ω-balanced topological groups
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DOI: 10.1016/j.topol.2017.02.029
Abstract: Abstract We give sufficient conditions under which a topological group is topologically isomorphic to a subgroup of a product of strongly metrizable topological groups. We introduce the concept of strongly δ -complete topological group and… read more here.
Keywords: topology; balanced topological; topological groups; strongly balanced ... See more keywords
Some properties of topological groups related to compactness
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DOI: 10.1016/j.topol.2017.02.039
Abstract: Abstract In the present article four problems from the A.V. Arhangel'skii and M.G. Tkachenko's book [8] are examined. Theorem 2.5 affirms that for any uncountable cardinal τ there exists a zero-dimensional hereditarily paracompact non-metrizable Abelian… read more here.
Keywords: groups related; topological groups; topological group; properties topological ... See more keywords
On spaces continuously containing topological groups
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DOI: 10.1016/j.topol.2020.107072
Abstract: Abstract In this paper we study some properties of the so-called spaces continuously containing topological groups, which were introduced as an alternative of the notion of universal topological groups. read more here.
Keywords: containing topological; topological groups; topology; spaces continuously ... See more keywords
Properties of remainders of topological groups and of their perfect images
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DOI: 10.1016/j.topol.2021.107687
Abstract: Abstract If X is a dense subspace of a space B, then B is called an extension of X, and the subspace Y = B ∖ X is called a remainder of X. We study… read more here.
Keywords: perfect images; remainders topological; topological groups; subspace ... See more keywords
Normality in Free Topological Groups
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DOI: 10.1134/s0001434618070283
Abstract: It is shown that, under the assumption of the continuum hypothesis, the normality of all finite powers of a topological space does not imply the normality of its free topological group. read more here.
Keywords: free topological; topological groups; normality free;
Cross-complementary subsets in paratopological groups
Sign Up to like & getrecommendations! Published in 2018 at "Hacettepe Journal of Mathematics and Statistics"
DOI: 10.15672/hjms.2018.647
Abstract: The following general question is considered by A.V. Arhangel’skiˇi [Perfect mappings in topological groups, cross-complementary subsets and quotients, Comment. Math.Univ.Carolin., 2003]. Suppose that G is a topological group, and F,M are subspaces of G such… read more here.
Keywords: complementary subsets; arhangel ski; topological groups; cross complementary ... See more keywords
On topological groups with an approximate fixed point property.
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DOI: 10.1590/0001-3765201720150382
Abstract: A topological group G has the Approximate Fixed Point (AFP) property on a bounded convex subset C of a locally convex space if every continuous affine action of G on C admits a net (… read more here.
Keywords: topological groups; property; groups approximate; approximate fixed ... See more keywords
The G-connected property and G-topological groups
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DOI: 10.2298/fil1914441w
Abstract: In this paper, we discuss some properties of of G-hull, G-kernel and G-connectedness, and extend some results of [28]. In particular, we prove that the G-connectedness are preserved by countable product. Moreover, we introduce the… read more here.
Keywords: topology; connected property; topological groups; property topological ... See more keywords
Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups
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DOI: 10.3390/axioms10030167
Abstract: This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of… read more here.
Keywords: continuous characters; factoring continuous; characters defined; topological groups ... See more keywords