Universal absolute extensors in extension theory

Karasev, A.; Valov, Vesko

doi:10.1090/s0002-9939-06-08304-3

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X-connectedness and λ-Boundedness1

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2007

2008

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Cited by 4 publications

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“…Next is Definition 6.1 of [16]. As mentioned there, this should be compared with similar ones given in [9], [10], and [11]. Definition 4.1.…”

Section: X-connectedness and λ-Boundednessmentioning

confidence: 99%

Extension theory and the $\Psi^\infty$ operator

Ivanšić¹,

Rubin²

2008

Publ. Math. Debrecen

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We are going to define for each simplicial complex K, an operator Ψ ∞ on the subcomplexes of K. If one is given a collection of spaces, closed subspaces of them, and maps of the closed subspaces to a subpolyhedron of |K| that extend to maps into |K|, then we are going to use the Ψ ∞ operator to help determine a subcomplex of minimal cardinality into which the maps can be extended simultaneously.The question (raised by A. Dranishnikov and J. Dydak) of whether the extension dimension, extdim (C,T ) X, has a countable representative when X is compact and metrizable, C is the class of compact metrizable spaces, and T is the class of CW-complexes is an unsolved problem. We shall define an "anti-basis" for a CW-complex and use this along with the Ψ ∞ operator to allow one to view this problem from another perspective.

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“…Next is Definition 6.1 of [16]. As mentioned there, this should be compared with similar ones given in [9], [10], and [11]. Definition 4.1.…”

Section: X-connectedness and λ-Boundednessmentioning

confidence: 99%