Group topologies on the real line
Jen-chung Chuan,Li Liu +1 more
TLDR
In this article, it was shown that 2 2 c non-isomorphic group topologies on the real line are non-locally compact, connected, locally compact and compactly generated.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1981-06-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Comparison of topologies & Real line.read more
Citations
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Counting compact group topologies
W. Wistar Comfort,Dieter Remus +1 more
TL;DR: In this article, the authors revisited Halmos, Hulanicki, Fuchs, Hawley, Chuan/Liu, Kirku, and Shtern's results on the cardinalities of a pairwise non-homeomorphic subset of cgt (K) for a group K = κ ≥ ω.
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Topologies on the real line
Manuel A. Mulero,B. Requejo +1 more
TL;DR: In this article , it was shown that if a topology on the real line endows it with a topological group structure (additive) for which the interval $$(0,+\infty )$$ is an open set, then this topology is stronger than the usual topology.
References
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Book
Abstract Harmonic Analysis
Edwin Hewitt,Kenneth A. Ross +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
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Comment on the real line
TL;DR: In this article, it was shown that the additive group of rationals can be topologized so that it can become a compact topological group, and the existence of such a topological topology can be proven.
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On the number of field topologies on an infinite field
TL;DR: In this article, it was shown that every uncountable infinite field admits 2210 different field topologies, no two of which are topologically isomorphic, and the latter result was generalized to any infinite commutative ring without proper zero-divisors.
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Homeomorphism and Isomorphism of Abelian Groups
TL;DR: In this article, the question of whether the topological group structure is determined by these weaker structures was considered and it was shown that if G 1 and G 2 are locally compact and connected, then G 1 ≈ G 2 implies G 1 = G 2.