Inverse limits of compact spaces
نویسندگان
چکیده
منابع مشابه
On Inverse Limits of Compact Spaces. Correction of a Proof
For a compact Hausdorff space X and an ANR for metrizable spaces M , one considers the space M of all mappings from X to M , endowed with the compact-open topology. Since a mapping f : X → X induces a natural mapping M : M → M ′ , an inverse system of compact Hausdorff spaces X determines a direct system M of spaces as well as the corresponding direct system of singular homology groups Hn(M ;G)...
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Let M be an arbitrary Riemannian homogeneous space, and let Ω be a space of tilings of M , with finite local complexity (relative to some symmetry group Γ) and closed in the natural topology. Then Ω is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Γ. This ...
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If B is an infinite subset of ω and X is a topological group, let CX B be the set of all x ∈ X such that 〈xn : n ∈ B〉 converges to 1. If F is a filter of infinite sets, let DX F = ⋃{CX B : B ∈ F}. The CX B and DX F are subgroups of X when X is abelian. In the circle group T, it is known that CX B always has measure 0. We show that there is a filter F such that DT F has measure 0 but is not cont...
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We continue the investigation of CW homotopy type of spaces of continuous functions between two CW complexes begun by J. Milnor in 1959 and P. Kahn in 1984. Viewing function spaces as particular cases of inverse limits we also study certain inverse systems of fibrations between CW homotopy type spaces. If the limit space Z∞ of an inverse sequence {Zi} of fibrations between CW type spaces has CW...
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We study direct limits (G,K) = lim −→ (Gn,Kn) of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicityfree discrete direct sum of irreducible representations. Then we look at direct limits G/K = lim −→ Gn/Kn of compact riemannian symmetric spaces, where we combine our criterion with the Cartan–Helgason theorem to show in general that the reg...
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ژورنال
عنوان ژورنال: General Topology and its Applications
سال: 1979
ISSN: 0016-660X
DOI: 10.1016/0016-660x(79)90008-4