Varieties of topological groups a survey

Morris, Sidney A.

doi:10.4064/cm-46-2-147-165

Cited by 30 publications

(29 citation statements)

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“…Since A is absolutely productive, there exists f ∈ C p (X, R) such that f = lim k→∞ k i=0 z(i)f i . From (19) and (20) we get f (x n ) = n i=0 z(i)f i (x n ) > n for every n ∈ N. Thus, the function f is unbounded on X, and so X is not pseudocompact.…”

mentioning

confidence: 99%

Group-valued continuous functions with the topology of pointwise convergence

Shakhmatov

Spěvák²

2010

Topology and its Applications

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mentioning

confidence: 99%

Group-valued continuous functions with the topology of pointwise convergence

Shakhmatov

Spěvák²

2010

Topology and its Applications

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“…If A is a class of Hausdorff groups, there is a smallest variety V(A) of Hausdorff groups such that A is a subclass of V(A). If, in addition to the operations above, (P) denotes the formation of finite cartesian products and (S) the formation of closed subgroups, it can be shown that V(A) = SCQ SP(A), see [4], Theorem 2, also [25], Theorem 7. Since finite products, closed subgroups, and Hausdorff quotients of K-Lie groups are K-Lie groups, the variety of Hausdorff groups generated by the class of K-Lie groups has the form V(LIE K ) = SC(LIE K ) (1) (see [16], [9]).…”

Section: Lemma 43 η Gmentioning

confidence: 99%

Real and p-adic Lie algebra functors on the category of topological groups

Glöckner¹

2002

Pacific J. Math.

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We define real and p-adic topological Lie algebra functors on the category of topological (Hausdorff) groups which extend the usual Lie algebra functors on the categories of real resp. p-adic Lie groups, and study their properties. 0. Introduction. We define real and p-adic topological Lie algebra functors on the category of topological (Hausdorff) groups which extend the usual Lie algebra functors. The method is a refinement of ideas developed in Lashof [20], which allow the set Hom(R, G) of one-parameter subgroups to be made into a real topological Lie algebra, for every topological group G whose identity component G 0 is a pro-Lie group. The main goals are the following.

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“…This complete characterization of the non-Archimedean groups is a part of Theorem 3.3 below. It is easy to show that the class of all nonArchimedean groups is a variety in the sense of [12]. That is, this class is closed under the formation of topological subgroups, products and quotient groups.…”

Section: Fact 11 Every Non-empty Compact Zero-dimensional Metrimentioning

confidence: 99%