# 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

top- [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 Zbl1050.54009
- [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
- [4] Curtis D., Hyperspaces of noncompact metric spaces, Compositio Math., 1980, 40, 139–152 Zbl0431.54004
- [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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