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The fundamental group as a topological group [PDF]

Topology and its Applications, 2012
This paper is devoted to the study of a natural group topology on the fundamental group which remembers local properties of spaces forgotten by covering space theory and weak homotopy type.
Brazas, Jeremy
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Each topological group embeds into a duoseparable topological group [PDF]

Topology and its Applications, 2021
9 ...
Alex Ravsky, Igor Guran, Taras Banakh, Taras Banakh   +3 more
arxiv   +6 more sources

The topological fundamental group and free topological groups [PDF]

Topology and its Applications, 2010
The topological fundamental group $\pi_{1}^{top}$ is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces which admit universal covers.
Aguilar, Arhangel'skii, Biss, Calcut, Cannon, Carlsson, Dugundji, Eda, Fabel, Fabel, Fabel, Fabel, Fay, Fischer, Fischer, Ghane, Ghane, Ghane, Harris, Hurewicz, Jeremy Brazas, Mack, Mal'tsev, Mardesic, May, Munkres, Sahleh, Sipacheva, Thomas   +28 more
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Ambitable topological groups [PDF]

Topology and its Applications, 2008
A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit.
Arkhangelskiıˇ, Berezanskiıˇ, Berglund, Bouziad, de Vries, Fedorova, Ferri, Glasner, Guran, Jan Pachl, Jech, Lau, Lau, Megrelishvili, Neufang, Neumann, Pachl, Protasov, Uspenskij, Uspenskij   +19 more
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Continuity in Topological Groups [PDF]

Proceedings of the American Mathematical Society, 1962
1. In the theory of topological groups, it is customary to make certain assumptions concerning the continuity of the product and continuity of the inverse. It has been noted that certain types of group spaces with less stringent assumptions than those usually made yield the ordinary assumptions [1; 2; 3; 4; 5].
Ta-Sun Wu
openalex   +3 more sources

Klein Topological Field Theories from Group Representations [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers.
Sergey A. Loktev, Sergey M. Natanzon
doaj   +5 more sources

On Central Topological Groups [PDF]

Transactions of the American Mathematical Society, 1967
Siegfried Grosser, Martin Moskowitz
openalex   +4 more sources

Topologically orderable groups

General Topology and its Applications, 1975
AbstractTopological groups whose topology can be induced by a total order are characterized up to homeomorphism. In particular, a non-metrizable topological group is in this class if and only if it has a totally ordered base at the identity consisting of (closed and) open subgroups.
Peter Nyikos, Hans‐Christian Reichel
openalex   +3 more sources

On p-topological groups [PDF]

Mathematica Moravica, 2021
In this paper, we introduce the notions of p-topological group and p-irresolute topological group which are generalizations of the notion topological group.
Jafari Saeid, Gnanachandra Paulraj, Kumar Arumugam Muneesh   +2 more
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ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS [PDF]

Journal of Algebraic Systems, 2020
. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV.
M. R. Ahmadi Zand, S. Rostami
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