Free topological vector spaces

Joe Flood

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Displaying similar documents to “Free topological vector spaces”

On free topological algebras

Hans-E. Porst (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Open subgroups of free topological groups

Jeremy Brazas (2014)

Fundamenta Mathematicae

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The theory of covering spaces is often used to prove the Nielsen-Schreier theorem, which states that every subgroup of a free group is free. We apply the more general theory of semicovering spaces to obtain analogous subgroup theorems for topological groups: Every open subgroup of a free Graev topological group is a free Graev topological group. An open subgroup of a free Markov topological group is a free Markov topological group if and only if it is disconnected.

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

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Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

The nucleus of the free alternative algebra.

Hentzel, I.R., Peresi, L.A. (2006)

Experimental Mathematics

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Square-free and overlap-free words

A. J. Kfoury (1988)

Banach Center Publications

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Generalized sum-free subsets.

Caro, Yair (1990)

International Journal of Mathematics and Mathematical Sciences

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Some Recent Results on Squarefree Words

Jean Berstel (1985)

Publications du Département de mathématiques (Lyon)

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A relatively free topological group that is not varietal free

Vladimir Pestov, Dmitri Shakhmatov (1998)

Colloquium Mathematicae

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Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.