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Extending Topological Abelian Groups by the Unit Circle

Abstract and Applied Analysis, 2013
A twisted sum in the category of topological Abelian groups is a short exact sequence 0→Y→X→Z→0 where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to 0→Y→Y×Z→Z→0.
Hugo J. Bello +2 more
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On Non-Archimedean Fuzzy Metric Free Topological Groups

Axioms
We construct the free group over a non-Archimedean fuzzy metric space (X,M,∧) in the sense of George and Veeramani where ∧ is the minimum t-norm. The two main tools used are the concept of a scheme (for every non-empty subset S of N of even cardinal, a ...
Cristina Bors, Manuel Sanchis
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Free products of topological groups and $M$-equivalence

Математичні Студії
In the paper we apply free products of topological groups for investigating the $M$-equivalence of Tychonoff spaces which are infinite disjoint sums of its subspaces. The main result is the following: Let $X=\overset{\infty}{\underset{i=1}{\oplus}}X_{i}$
N. M. Pyrch
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Robustness of Topological Phases on Aperiodic Lattices. [PDF]

Math Phys Anal Geom
Li Y.
europepmc +1 more source

Aberrant topology of the default mode network is associated with phosphatidylcholine and triglyceride levels in major depressive disorder. [PDF]