Openness of Induced Mappings

J. J. Charatonik; W. J. Charatonik; Alejandro Illanes

doi:10.1016/S0166-8641(99)00042-5

Openness of Induced Mappings

J. J. Charatonik
, W. J. Charatonik
, Alejandro Illanes

Missouri University of Science and Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X→Y the induced mapping C(f):C(X)→C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f:X×Y→X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.

Original language	American English
Journal	Topology and its Applications
DOIs	https://doi.org/10.1016/S0166-8641(99)00042-5
State	Published - Nov 1 1999

Keywords

Continuum
Dendrites
Hyperspace
Induced Mapping
Open

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1016/S0166-8641(99)00042-5

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title = "Openness of Induced Mappings",

abstract = " Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X→Y the induced mapping C(f):C(X)→C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f:X×Y→X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.",

keywords = "Continuum, Dendrites, Hyperspace, Induced Mapping, Open",

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doi = "10.1016/S0166-8641(99)00042-5",

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T1 - Openness of Induced Mappings

AU - Charatonik, J. J.

AU - Charatonik, W. J.

AU - Illanes, Alejandro

PY - 1999/11/1

Y1 - 1999/11/1

N2 - Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X→Y the induced mapping C(f):C(X)→C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f:X×Y→X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.

AB - Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X→Y the induced mapping C(f):C(X)→C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f:X×Y→X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.

KW - Continuum

KW - Dendrites

KW - Hyperspace

KW - Induced Mapping

KW - Open

UR - https://scholarsmine.mst.edu/math_stat_facwork/128

UR - https://doi.org/10.1016/S0166-8641(99)00042-5

U2 - 10.1016/S0166-8641(99)00042-5

DO - 10.1016/S0166-8641(99)00042-5

M3 - Article

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Openness of Induced Mappings

Abstract

Keywords

Disciplines

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