# Conditions which ensure that a simple map does not raise dimension

Colloquium Mathematicae (1992)

- Volume: 63, Issue: 2, page 173-185
- ISSN: 0010-1354

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topDębski, W., and Mioduszewski, J.. "Conditions which ensure that a simple map does not raise dimension." Colloquium Mathematicae 63.2 (1992): 173-185. <http://eudml.org/doc/210143>.

@article{Dębski1992,

abstract = {The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps from them do not raise dimension. In what follows a map means a continuous map, unless explicitly stated otherwise. A space is, except in some general lemmas, understood to be metrizable. A compactum means a compact metric space.},

author = {Dębski, W., Mioduszewski, J.},

journal = {Colloquium Mathematicae},

keywords = {2-to-1 map; dimension-raising map; dendrite; pair of twins; simple map},

language = {eng},

number = {2},

pages = {173-185},

title = {Conditions which ensure that a simple map does not raise dimension},

url = {http://eudml.org/doc/210143},

volume = {63},

year = {1992},

}

TY - JOUR

AU - Dębski, W.

AU - Mioduszewski, J.

TI - Conditions which ensure that a simple map does not raise dimension

JO - Colloquium Mathematicae

PY - 1992

VL - 63

IS - 2

SP - 173

EP - 185

AB - The present paper deals with those continuous maps from compacta into metric spaces which assume each value at most twice. Such maps are called here, after Borsuk and Molski (1958) and as in our previous paper (1990), simple. We investigate the possibility of decomposing a simple map into essential and elementary factors, and the so-called splitting property of simple maps which raise dimension. The aim is to get insight into the structure of those compacta which have the property that simple maps from them do not raise dimension. In what follows a map means a continuous map, unless explicitly stated otherwise. A space is, except in some general lemmas, understood to be metrizable. A compactum means a compact metric space.

LA - eng

KW - 2-to-1 map; dimension-raising map; dendrite; pair of twins; simple map

UR - http://eudml.org/doc/210143

ER -

## References

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