Open Mappings Increasing Order

J. J. Charatonik; W. J. Charatonik

doi:10.1090/S0002-9939-97-04096-3

Open Mappings Increasing Order

J. J. Charatonik
, W. J. Charatonik

Missouri University of Science and Technology

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

Abstract

It is shown that an analog of Whyburn's theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.

Original language	American English
Journal	Proceedings of the American Mathematical Society
DOIs	https://doi.org/10.1090/S0002-9939-97-04096-3
State	Published - Jan 1 1997

Keywords

classical sense
confluent
continuum
dendroid
light
open mapping
order
smooth

Disciplines

Mathematics
Statistics and Probability

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https://doi.org/10.1090/S0002-9939-97-04096-3

Cite this

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abstract = " It is shown that an analog of Whyburn's theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.",

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AB - It is shown that an analog of Whyburn's theorem saying that open mappings do not increase order of a point of locally compact metric spaces is not true if the Menger-Urysohn order is replaced by order in the classical sense. On the other hand, this analog is true, even for a wider class of confluent mappings, under an additional condition that the mapping is light and the domain continuum is hereditarily unicoherent.

KW - classical sense

KW - confluent

KW - continuum

KW - dendroid

KW - light

KW - open mapping

KW - order

KW - smooth

UR - https://scholarsmine.mst.edu/math_stat_facwork/336

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M3 - Article

SN - 1088-6826

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -

Open Mappings Increasing Order

Abstract

Keywords

Disciplines

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