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A characterization of cubes and spheres

100%

Szymański A., Turzański M.

Instytut Matematyczny Polskiej Akademii Nauk

EN

Contents Introduction.................................................................................................................... 5 § 1. BlSC-subbases..................................................................................................... 6 § 2. The families D(U) and C(U) and the spaces $X_U$ for a given U.............. 7 § 3. A lemma on chains in maximal BISC-subbases of continua...................... 9 § 4. Further properties of the spaces $X_U$.......................................................... 12 § 5. The Main Lemma.................................................................................................. 14 § 6. Application to the characterization of several cubes...................................... 16 $ 7. Topological characterization of n-spheres....................................................... 17 References.................................................................................................................... 29

2

On absolute retracts of ω*

75%

Bella A., Błaszczyk A., Szymański A.

Fundamenta Mathematicae

|

1994

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tom 145

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nr 1

1-13

EN

An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight $ω_1$ is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same π-weight), then X is homeomorphic to the Gleason space over the Cantor cube ${0,1}^{ω_1}$.

3

On intersections of sets of positive Lebesgue measure

56%

Cichoń J., Szymański A., Węglorz B.

Colloquium Mathematicum

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1987

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tom 52

|

nr 2

173-174

4

There are absolute ultrafilters on N which are not minimal

56%

Kucia A., Szymański A.

Colloquium Mathematicum

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1977

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tom 37

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nr 1

29-34

5

Continua with a connected set of points of indecomposability

56%

Emeryk A., Szymański A.

Colloquium Mathematicum

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1977

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tom 37

|

nr 2

185-191

6

The existence of $P(α)$-points of N* for $ℵ_0α<{\germ c}$

55%

Szymański A.

Colloquium Mathematicum

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1977

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tom 37

|

nr 2

179-184

7

Accumulation points of nowhere dense sets

47%

Kulpa W., Szymański A.

Colloquium Mathematicum

|

1974-1975

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tom 32

|

nr 1

69-70

8

Compact metric spaces have binary bases

47%

Strok M., Szymański A.

Fundamenta Mathematicae

|

1975

|

tom 89

|

nr 1

81-91

9

On Blumberg type spaces

38%

Kulpa W., Szymański A.

Colloquium Mathematicum

|

1981

|

tom 45

|

nr 2

215-219

Ograniczanie wyników

6 Colloquium Mathematicum

2 Fundamenta Mathematicae

9 Szymański A.

2 Kulpa W.

1 Bella A.

1 Błaszczyk A.

1 Cichoń J.

1 Emeryk A.

1 Kucia A.

1 Strok M.

1 Turzański M.

1 Węglorz B.

1 1994

1 1987

1 1981

3 1977

1 1975

2 1974

A characterization of cubes and spheres

On absolute retracts of ω*

On intersections of sets of positive Lebesgue measure

There are absolute ultrafilters on N which are not minimal

Continua with a connected set of points of indecomposability

The existence of $P(α)$-points of N* for $ℵ_0α<{\germ c}$

Accumulation points of nowhere dense sets

Compact metric spaces have binary bases

On Blumberg type spaces