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1

Conditions which ensure that a simple map does not raise dimension

100%

Dębski W., Mioduszewski J.

Colloquium Mathematicum

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1992

|

tom 63

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nr 2

173-185

EN

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.

2

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Simple plane images of the Sierpiński triangular curve are nowhere dense

70%

Dębski W., Mioduszewski J.

Colloquium Mathematicum

|

1990

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tom 59

|

nr 1

125-140

3

Another geometric proof of supercompactness of compact metric spaces

70%

Dębski W.

Colloquium Mathematicum

|

1984

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tom 48

|

nr 2

205-208

4

On topological types of the simplest indecomposable continua

60%

Dębski W.

Colloquium Mathematicum

|

1984-1985

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tom 49

|

nr 2

203-211

5

The additivity of the volume and Sperner's lemma

50%

Dębski W.

Colloquium Mathematicum

|

1990

|

tom 59

|

nr 1

117-123

Ograniczanie wyników

5 Colloquium Mathematicum

5 Dębski W.

2 Mioduszewski J.

1 1992

2 1990

1 1985

1 1984

Conditions which ensure that a simple map does not raise dimension

Simple plane images of the Sierpiński triangular curve are nowhere dense

Another geometric proof of supercompactness of compact metric spaces

On topological types of the simplest indecomposable continua

The additivity of the volume and Sperner's lemma