Minimal and precompact group topologies on free groups
نویسندگان
چکیده
منابع مشابه
Minimal Pseudocompact Group Topologies on Free Abelian Groups
A Hausdorff topological group G is minimal if every continuous isomorphism f : G → H between G and a Hausdorff topological group H is open. Significantly strengthening a 1981 result of Stoyanov we prove the following theorem: For every infinite minimal group G there exists a sequence {σn : n ∈ N} of cardinals such that w(G) = sup{σn : n ∈ N} and sup{2 σn : n ∈ N} ≤ |G| ≤ 2, where w(G) is the we...
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It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology. Introduction For a topological group G, the group G of continuous homomorphisms (characters) into the torus T = {z ∈ C : |z| = 1} endowed with the compact-open topology is called the character group of G and G is named Pontryagin reflexive or reflexive if the canonical homomorphism ...
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The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1991
ISSN: 0022-4049
DOI: 10.1016/0022-4049(91)90014-s