Unbounded sets of maps and compactification in extension theory

Rubin, Leonard R.

doi:10.1016/j.topol.2007.08.012

Cited by 5 publications

(7 citation statements)

References 11 publications

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“…For theorem 7.6 of [22], the 'cycle' of implications (d) =⇒ (e) =⇒ (f) =⇒ (c) =⇒ (d) can also be deduced from our results in the following way. The equivalence (b) ⇐⇒ (c) of [22] shows, in our language, that a CW complex K is weakly quasi-finite with respect to the ℵ 0 -saturation of compact metric spaces if and only if K is weakly quasi-finite with respect to the (total) saturation of the class of compact metric spaces. We consider that result very interesting.…”

Section: Geometric Properties Of Quasi-finite Cw Complexesmentioning

confidence: 56%

“…In [7] Dranishnikov and Repovš introduced the concept of Xτ (L, K), where K ⊂ L. It means that any map f : A → K, with A closed in X, extends to g : X → L. Rubin (see [22], Definition 6.1) says in that case that the pair (L, K) is X-connected. In [5] Dranishnikov considers the concept of Xτ i, where i : K → L is a map.…”

Section: Extension Properties Of Families Of Mapsmentioning

confidence: 99%

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Compact maps and quasi-finite complexes

Cencelj¹,

Dydak²,

Smrekar³

et al. 2007

Topology and its Applications

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Section: Geometric Properties Of Quasi-finite Cw Complexesmentioning

confidence: 56%

Section: Extension Properties Of Families Of Mapsmentioning

confidence: 99%

Compact maps and quasi-finite complexes

Cencelj¹,

Dydak²,

Smrekar³

et al. 2007

Topology and its Applications

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“…Definitions needed to describe such a problem and others more general than it along with some rudimentary results, e.g., Corollary 2.9, about such extensions can be found in Section 2 below. A situation like this was encountered in [16] where the author (see Proposition 2.4 of that citation) determined a relationship between that kind of extension problem and whether βXτ K.…”

Section: Introductionmentioning

confidence: 94%

“…Let us recall Definition 2.1 of [16]; we use a slightly different terminology in order to conform to the needs of this paper. Definition 2.2.…”

Section: λ-Bounded Collections Of Mapsmentioning

confidence: 99%

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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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Identification of potential sites of debris flows in the upper Min River drainage, following environmental changes caused by the Wenchuan earthquake

et al. 2010

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The Wenchuan earthquake caused numerous landslides and collapses that provide abundant unconsolidated material for future mobilization as debris flows. Debris flows will be very active and cause considerable damage for some time in the affected area. Because of environmental changes related to the earthquake, many potentially dangerous debris flow gullies have yet to be identified. This paper selects the upper Min River from Yinxiu to Wenchuan as the study area, interprets the unconsolidated deposits, and discusses their relationship to distance from the fault. Then, applying that information and the values of other factors relating to debris flow occurrence, the locations of potential debris flows are analyzed by multi-factor comprehensive identification and rapid identification. The multi-factor comprehensive identification employs fuzzy matter-element extension theory. The volume of unconsolidated material in the study area is about 3.28 × 10 8 m 3 . According to the analysis by multi-factor comprehensive identification, 47 gullies have a high probability for potential debris flow, 8 gullies have a moderate probability, and 1 gully has a low probability.

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Unbounded sets of maps and compactification in extension theory

Cited by 5 publications

References 11 publications

Compact maps and quasi-finite complexes

Compact maps and quasi-finite complexes

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

Identification of potential sites of debris flows in the upper Min River drainage, following environmental changes caused by the Wenchuan earthquake

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