Pseudo-arcs and connectedness in homeomorphism groups

Wayne Lewis

doi:10.1090/S0002-9939-1983-0687655-1

Pseudo-arcs and connectedness in homeomorphism groups

Wayne Lewis

Mathematics and Statistics

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

14 Scopus citations

Abstract

We prove that the homeomorphism group of the pseudo-arc contains no nondegeneratc continua. An equivalent result holds for any continuum all of whose small subcontinua are pseudo-arcs. e.g. for the pseudo-circle and the circle of pseudo-arcs. Related questions arc briefly mentioned.

Original language	English
Pages (from-to)	745-748
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	87
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1983-0687655-1
State	Published - Apr 1983

Keywords

Continuum
Hereditary indccomposability
Homeomorphism group
Homogeneity
Pseudo-arc

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10.1090/S0002-9939-1983-0687655-1

Cite this

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title = "Pseudo-arcs and connectedness in homeomorphism groups",

abstract = "We prove that the homeomorphism group of the pseudo-arc contains no nondegeneratc continua. An equivalent result holds for any continuum all of whose small subcontinua are pseudo-arcs. e.g. for the pseudo-circle and the circle of pseudo-arcs. Related questions arc briefly mentioned.",

keywords = "Continuum, Hereditary indccomposability, Homeomorphism group, Homogeneity, Pseudo-arc",

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N2 - We prove that the homeomorphism group of the pseudo-arc contains no nondegeneratc continua. An equivalent result holds for any continuum all of whose small subcontinua are pseudo-arcs. e.g. for the pseudo-circle and the circle of pseudo-arcs. Related questions arc briefly mentioned.

AB - We prove that the homeomorphism group of the pseudo-arc contains no nondegeneratc continua. An equivalent result holds for any continuum all of whose small subcontinua are pseudo-arcs. e.g. for the pseudo-circle and the circle of pseudo-arcs. Related questions arc briefly mentioned.

KW - Continuum

KW - Hereditary indccomposability

KW - Homeomorphism group

KW - Homogeneity

KW - Pseudo-arc

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U2 - 10.1090/S0002-9939-1983-0687655-1

DO - 10.1090/S0002-9939-1983-0687655-1

M3 - Article

AN - SCOPUS:84966237094

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EP - 748

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 4

ER -

Pseudo-arcs and connectedness in homeomorphism groups

Abstract

Keywords

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