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American Journal of Mathematics
Article . 1981 . Peer-reviewed
Data sources: Crossref
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Cech Homology Characterizations of Infinite Dimensional Manifolds

Čech homology characterizations of infinite dimensional manifolds
Authors: Daverman, Robert J.; Walsh, John J.;

Cech Homology Characterizations of Infinite Dimensional Manifolds

Abstract

Let \(X\) denote a locally compact ANR. It is shown that \(X\) is a \(Q\)-manifold if and only if \(X\) has the disjoint disks property and the disjoint Čech carriers property. This result can be regarded as the infinite- dimensional version of the known fact that when \(n\geq 5\), a generalized n-manifold Y is a topological \(n\)-manifold if and only if \(Y\) has the disjoint disk property; the proof relies on the result of \textit{H. Torunczyk} [Fundam. Math. 106, 31-40 (1980; Zbl 0346.57004)] that \(X\) is a \(Q\)-manifold if and only if \(X\) has the disjoint \(k\)-cells property for each \(k\geq 0\). Several applications are given to the problems of recognizing \(Q\)-manifolds among products, proper cell-like images of \(Q\)-manifolds, and sums of \(Q\)-manifolds. An example is also given of a cellular decomposition of \(Q\) whose nondegenerate elements form a null-sequence, but whose decomposition space is not a \(Q\)-manifold.

Keywords

infinite codimension, Cellularity in topological manifolds, cellular decomposition, decomposition space, Steenrod-Sitnikov homologies, Topology of infinite-dimensional manifolds, disjoint disks property, disjoint Čech carriers property, Homotopy and topological questions for infinite-dimensional manifolds, Generalized manifolds, locally compact ANR, Q-manifold

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Average
Top 10%
Top 10%
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