The ANR-property of hyperspaces with the Attouch-Wets topology
Open Mathematics (2008)
- Volume: 6, Issue: 2, page 228-236
- ISSN: 2391-5455
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topRostyslav Voytsitskyy. "The ANR-property of hyperspaces with the Attouch-Wets topology." Open Mathematics 6.2 (2008): 228-236. <http://eudml.org/doc/269352>.
@article{RostyslavVoytsitskyy2008,
abstract = {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.},
author = {Rostyslav Voytsitskyy},
journal = {Open Mathematics},
keywords = {hyperspace; Attouch-Wets topology; ANR},
language = {eng},
number = {2},
pages = {228-236},
title = {The ANR-property of hyperspaces with the Attouch-Wets topology},
url = {http://eudml.org/doc/269352},
volume = {6},
year = {2008},
}
TY - JOUR
AU - Rostyslav Voytsitskyy
TI - The ANR-property of hyperspaces with the Attouch-Wets topology
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 228
EP - 236
AB - 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.
LA - eng
KW - hyperspace; Attouch-Wets topology; ANR
UR - http://eudml.org/doc/269352
ER -
References
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- [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 Zbl1125.54006
- [3] Beer G., Topologies on closed and closed convex sets, MIA 268, Kluwer Academic Publishers Group, Dordrecht, 1993 Zbl0792.54008
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- [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 Zbl1056.54015
- [7] Voytsitskyy R., Hyperspaces with the Attouch-Wets topology homeomorphic to ℓ2, http://arxiv.org/abs/0803.2098 Zbl1164.54009
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