Images of the Cantor Fan

J. J. Charatonik; W. J. Charatonik

doi:10.1016/S0166-8641(89)80005-7

Images of the Cantor Fan

J. J. Charatonik
, W. J. Charatonik

Missouri University of Science and Technology

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

Abstract

Structural characterizations are obtained of images of the Cantor fan (i.e., the cone over the Cantor set) under mappings that belong to one of the following classes: confluent, open, monotone, retractions, light, and any intersections of these. A necessary and sufficient condition is shown under which there exists a monotone mapping from an arbitrary fan onto an arc.

Original language	American English
Journal	Topology and its Applications
DOIs	https://doi.org/10.1016/S0166-8641(89)80005-7
State	Published - Jan 1 1989

Keywords

Cantor fan
arc
confluent
continuous
dendroid
end point
fan
image
light
monotone
open
property of Kelley
retract
smooth

Disciplines

Mathematics
Statistics and Probability

Access to Document

10.1016/S0166-8641(89)80005-7License: Unspecified

https://doi.org/10.1016/S0166-8641(89)80005-7

Cite this

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title = "Images of the Cantor Fan",

abstract = " Structural characterizations are obtained of images of the Cantor fan (i.e., the cone over the Cantor set) under mappings that belong to one of the following classes: confluent, open, monotone, retractions, light, and any intersections of these. A necessary and sufficient condition is shown under which there exists a monotone mapping from an arbitrary fan onto an arc.",

keywords = "Cantor fan, arc, confluent, continuous, dendroid, end point, fan, image, light, monotone, open, property of Kelley, retract, smooth",

author = "Charatonik, \{J. J.\} and Charatonik, \{W. J.\}",

year = "1989",

month = jan,

day = "1",

doi = "10.1016/S0166-8641(89)80005-7",

language = "American English",

journal = "Topology and its Applications",

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T1 - Images of the Cantor Fan

AU - Charatonik, J. J.

AU - Charatonik, W. J.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - Structural characterizations are obtained of images of the Cantor fan (i.e., the cone over the Cantor set) under mappings that belong to one of the following classes: confluent, open, monotone, retractions, light, and any intersections of these. A necessary and sufficient condition is shown under which there exists a monotone mapping from an arbitrary fan onto an arc.

AB - Structural characterizations are obtained of images of the Cantor fan (i.e., the cone over the Cantor set) under mappings that belong to one of the following classes: confluent, open, monotone, retractions, light, and any intersections of these. A necessary and sufficient condition is shown under which there exists a monotone mapping from an arbitrary fan onto an arc.

KW - Cantor fan

KW - arc

KW - confluent

KW - continuous

KW - dendroid

KW - end point

KW - fan

KW - image

KW - light

KW - monotone

KW - open

KW - property of Kelley

KW - retract

KW - smooth

UR - https://scholarsmine.mst.edu/math_stat_facwork/305

UR - https://doi.org/10.1016/S0166-8641(89)80005-7

U2 - 10.1016/S0166-8641(89)80005-7

DO - 10.1016/S0166-8641(89)80005-7

M3 - Article

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Images of the Cantor Fan

Abstract

Keywords

Disciplines

Access to Document

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