scholarly journals On the countable tightness and the k-property of free topological groups over generalized metrizable spaces

2016 ◽  
Vol 209 ◽  
pp. 198-206 ◽  
Author(s):  
Li-Hong Xie ◽  
Shou Lin ◽  
Piyu Li
Keyword(s):  
Topological Groups ◽  
Countable Tightness ◽  
Metrizable Spaces

scholarly journals Free topological groups over metrizable spaces

1989 ◽  
Vol 33 (1) ◽  
pp. 63-76 ◽  
Author(s):  
A.V. Arhangel'skiǐ ◽  
O.G. Okunev ◽  
V.G. Pestov
Keyword(s):  
Topological Groups ◽  
Metrizable Spaces

scholarly journals TheD-Property of Finite Unions oft-Metrizable Spaces and Certain Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xin Zhang ◽  
Hongfeng Guo
Keyword(s):  
Function Spaces ◽  
Countable Tightness ◽  
Metrizable Spaces

The additivity ofD-property is studied ont-metrizable spaces and certain function spaces. It is shown that a space of countable tightness is aD-space provided that it is the union of finitely manyt-metrizable subspaces, or function spacesCp(Xi)where eachXiis LindelöfΣ.

scholarly journals NOTES ON -TOPOLOGICAL GROUPS AND HOMEOMORPHISMS OF TOPOLOGICAL GROUPS

2012 ◽  
Vol 87 (3) ◽  
pp. 493-502 ◽  
Author(s):  
HANFENG WANG ◽  
WEI HE
Keyword(s):  
Topological Group ◽  
Affirmative Answer ◽  
Neutral Element ◽  
Topological Groups ◽  
Open Problems ◽  
Urysohn Space ◽  
Compact Topological Group ◽  
Countable Tightness

AbstractIn this paper, it is shown that there exists a connected topological group which is not homeomorphic to any $\omega $-narrow topological group, and also that there exists a zero-dimensional topological group $G$ with neutral element $e$ such that the subspace $X = G\setminus \{e\}$ is not homeomorphic to any topological group. These two results give negative answers to two open problems in Arhangel’skii and Tkachenko [Topological Groups and Related Structures (Atlantis Press, Amsterdam, 2008)]. We show that if a compact topological group is a $K$-space, then it is metrisable. This result gives an affirmative answer to a question posed by Malykhin and Tironi [‘Weakly Fréchet–Urysohn and Pytkeev spaces’, Topology Appl. 104 (2000), 181–190] in the category of topological groups. We also prove that a regular $K$-space $X$ is a weakly Fréchet–Urysohn space if and only if $X$has countable tightness.

SOME PROPERTIES OF G-SPACES ACTED WITH TOPOLOGICAL GROUPS

2020 ◽  
Vol 9 (7) ◽  
pp. 4917-4922
Author(s):  
S. Sivakumar ◽  
D. Lohanayaki
Keyword(s):  
Topological Groups
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