The ANR-property of hyperspaces with the Attouch-Wets topology

• Autorzy: Rostyslav Voytsitskyy
• Języki publikacji: EN

Abstrakty

EN

We characterize metric spaces whose hyperspaces of non-empty closed, bounded, compact or finite subsets, endowed with the Attouch-Wets topology, are absolute (neighborhood) retracts.

Słowa kluczowe

EN

hyperspace; Attouch-Wets topology; ANR

Kategorie tematyczne

• 54B20: Hyperspaces
• 54C55: Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 228-236

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Rostyslav Voytsitskyy

• Ivan Franko Lviv National University

Bibliografia

• [1] Banakh T., Kurihara M., Sakai K., Hyperspaces of normed linear spaces with the Attouch-Wets topology, Set-Valued Anal., 2003, 11, 21–36 http://dx.doi.org/10.1023/A:1021981321137
• [2] Banakh T., Voytsitskyy R., Characterizing metric spaces whose hyperspaces are absolute neighborhood retracts, Topology Appl., 2007, 154, 2009–2025 http://dx.doi.org/10.1016/j.topol.2006.02.009
• [3] Beer G., Topologies on closed and closed convex sets, MIA 268, Kluwer Academic Publishers Group, Dordrecht, 1993
• [4] Curtis D., Hyperspaces of noncompact metric spaces, Compositio Math., 1980, 40, 139–152
• [5] Curtis D., To Nhu N., Hyperspaces of finite subsets which are homeomorphic to ℵ0-dimensional linear metric spaces, Topol. Appl., 1985, 19, 251–260 http://dx.doi.org/10.1016/0166-8641(85)90005-7
• [6] Sakai K., Yaguchi M., Hyperspaces of Banach spaces with the Attouch-Wets topology, Set-Valued Anal., 2004, 12, 329–344 http://dx.doi.org/10.1023/B:SVAN.0000031354.48064.0b
• [7] Voytsitskyy R., Hyperspaces with the Attouch-Wets topology homeomorphic to ℓ2, http://arxiv.org/abs/0803.2098

Identyfikatory

DOI

10.2478/s11533-008-0022-z