Displaying similar documents to “Almost coproducts of finite cyclic groups”

Continuous selections on spaces of continuous functions

Angel Tamariz-Mascarúa (2006)

Commentationes Mathematicae Universitatis Carolinae

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For a space Z , we denote by ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) the hyperspaces of non-empty closed, compact, and subsets of cardinality ≤ 2 of Z , respectively, with their Vietoris topology. For spaces X and E , C p ( X , E ) is the space of continuous functions from X to E with its pointwise convergence topology. We analyze in this article when ℱ ( Z ) , 𝒦 ( Z ) and ℱ 2 ( Z ) have continuous selections for a space Z of the form C p ( X , E ) , where X is zero-dimensional and E is a strongly zero-dimensional metrizable space. We prove that C p ( X , E ) is weakly orderable...

On almost normal subgroups of supersoluble groups

Carmela Musella (1999)

Bollettino dell'Unione Matematica Italiana

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Un sottogruppo H di un gruppo G si dice «almost normal» se ha soltanto un numero finito di coniugati in G , e ovviamente l'insieme a ⁢ n ⁢ G costituito dai sottogruppi almost normal di G è un sottoreticolo del reticolo L ⁢ G di tutti i sottogruppi di G . In questo articolo vengono studiati gli isomorfismi tra reticoli di sottogruppi almost normal, provando in particolare che se G è un gruppo supersolubile e G ¯ è un gruppo FC-risolubile tale che i reticoli a ⁢ n ⁢ G e a ⁢ n ⁢ G ¯ sono isomorfi, allora anche G ¯ è supersolubile,...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

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On the unit sphere 𝕊 in a real Hilbert space 𝐇 , we derive a binary operation ⊙ such that ( 𝕊 , ⊙ ) is a power-associative Kikkawa left loop with two-sided identity 𝐞 0 , i.e., it has the left inverse, automorphic inverse, and A l properties. The operation ⊙ is compatible with the symmetric space structure of 𝕊 . ( 𝕊 , ⊙ ) is not a loop, and the right translations which fail to be injective are easily characterized. ( 𝕊 , ⊙ ) satisfies the left power alternative and left Bol identities “almost everywhere” but not...

Martin’s Axiom and ω -resolvability of Baire spaces

Fidel Casarrubias-Segura, Fernando Hernández-Hernández, Angel Tamariz-Mascarúa (2010)

Commentationes Mathematicae Universitatis Carolinae

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We prove that, assuming MA, every crowded T 0 space X is ω -resolvable if it satisfies one of the following properties: (1) it contains a π -network of cardinality < 𝔠 constituted by infinite sets, (2) χ ( X ) < 𝔠 , (3) X is a T 2 Baire space and c ( X ) ≤ ℵ 0 and (4) X is a T 1 Baire space and has a network 𝒩 with cardinality < 𝔠 and such that the collection of the finite elements in it constitutes a σ -locally finite family. Furthermore, we prove that the existence of a T 1 Baire irresolvable space is equivalent to the...