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    Wyświetlanie 1-3 z 3
    Tytuł:
    Deformations of bimodule problems
    Autorzy:
    Geiß, Christof
    Powiązania:
    https://bibliotekanauki.pl/articles/1205483.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    bimodule problems
    vector space categories
    tame
    wild
    deformations
    degenerations
    Opis:
    We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.
    Źródło:
    Fundamenta Mathematicae; 1996, 150, 3; 255-264
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convexity ranks in higher dimensions
    Autorzy:
    Kojman, Menachem
    Powiązania:
    https://bibliotekanauki.pl/articles/1205064.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    convexity
    convexity number
    Polish vector space
    continuum hypothesis
    Cantor-Bendixson degree
    Opis:
    A subset of a vector space is called countably convex if it is a countable union of convex sets. Classification of countably convex subsets of topological vector spaces is addressed in this paper. An ordinal-valued rank function ϱ is introduced to measure the complexity of local nonconvexity points in subsets of topological vector spaces. Then ϱ is used to give a necessary and sufficient condition for countable convexity of closed sets. Theorem. Suppose that S is a closed subset of a Polish linear space. Then S is countably convex if and only if there exists $α < ω_1$ so that ϱ(x) < α for all x ∈ S. Classification of countably convex closed subsets of Polish linear spaces follows then easily. A similar classification (by a different rank function) was previously known for closed subset of $ℝ^2$ [3]. As an application of ϱ to Banach space geometry, it is proved that for every $α < ω_1$, the unit sphere of C(ωα) with the sup-norm has rank α. Furthermore, a countable compact metric space K is determined by the rank of the unit sphere of C(K) with the natural sup-norm: Theorem. If $K_1,K_1$ are countable compact metric spaces and $S_i$ is the unit sphere in $C(K_i)$ with the sup-norm, i = 1,2, then $ϱ(S_1) = ϱ(S_2)$ if and only if $K_1$ and $K_2$ are homeomorphic. Uncountably convex closed sets are also studied in dimension n > 2 and are seen to be drastically more complicated than uncountably convex closed subsets of $ℝ^2$
    Źródło:
    Fundamenta Mathematicae; 2000, 164, 2; 143-163
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The concept of boundedness and the Bohr compactification of a MAP Abelian group
    Autorzy:
    Galindo, Jorge
    Hernández, Salvador
    Powiązania:
    https://bibliotekanauki.pl/articles/1205259.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Bohr topology
    LCA group
    $ℒ_∞$-group
    boundedness
    locally convex vector space
    DF-space
    maximally almost periodic
    respects compactness
    C-embedded
    C*-embedded
    Opis:
    Let G be a maximally almost periodic (MAP) Abelian group and let ℬ be a boundedness on G in the sense of Vilenkin. We study the relations between ℬ and the Bohr topology of G for some well known groups with boundedness (G,ℬ). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an $ℒ_∞$-group, contains "many" discrete C-embedded subsets which are C*-embedded in their Bohr compactification. This result generalizes an analogous theorem of van Douwen for the discrete case and some other ones due to Hartman and Ryll-Nardzewski concerning the existence of $I_0$-sets. We also obtain some results on preservation of compactness for the Bohr topology of several types of MAP Abelian groups, like $ℒ_∞$-groups, locally convex vector spaces and free Abelian topological groups.
    Źródło:
    Fundamenta Mathematicae; 1999, 159, 3; 195-218
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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