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Clan acts and codimension

Authors: Hofmann, K.H.; Day, J.M.;

Clan acts and codimension

Abstract

Let (T, X) be a continuum act, let cd X=n and suppose A is a T-ideal (i.e., a T-invariant subspace of X), such that Hn(A)≠0. We prove that A is a minimal T-ideal iff A=Gx for some x∈X and maximal group G in the minimal ideal of T. Moreover, if these conditions are satisfied, then A is the only minimal T-ideal and also is the unique floor for every nonzero element of Hn(X). We need and also prove here an improved version of the Tube Theorem [3], and this corollary: if (G, X) is an intransitive transformation group with G compact, X locally compact and finite dimensional, and X/G connected, then dimension Gx

Country
Germany
Related Organizations
Keywords

510.mathematics, Structure of topological semigroups, Transformation groups and semigroups (topological aspects), Article

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citations
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!
5
Average
Top 10%
Average
Green