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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Prime mappings, number of factors and binary operations

100%
van Douwen E. K.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Interesting mappings on finite powers..................................................... 5 2. Results.................................................................................................................... 6 3. Conventions and notation.................................................................................... 8 4. βω-spaces.............................................................................................................. 8 5. Canonical partition relations and the Prime Mapping Lemma.................... 9 6. The Number of Factors Lemma......................................................................... 11 7. Consequences of the Number of Factors Lemma......................................... 13 8. Direction of the coordinate axes......................................................................... 16 9. Binary operations................................................................................................... 18 10. Extension of binary operations.......................................................................... 21 11. Stronger versions of the Prime Mapping Lemma.......................................... 22 12. Extensions of binary operations on ω............................................................... 23 13. Examples................................................................................................................ 24 14. Appendix 1: An application of non-Q-points..................................................... 25 15. Appendix 3: Homeomorphs of βω in certain finite powers............................ 26 16. Appendix 3: Mappings onto βω-spaces............................................................ 28 17. Appendix 4: Square compactiiications.............................................................. 29 18. Appendix 5: Some points of interest.................................................................. 30 References.................................................................................................................... 34
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Remote points

100%
van Douwen E. K.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 0. Conventions................................................................................................................................... 5 1. Introduction............................................................................................................................................. 5 CHAPTER I. TOOLS AND THE CONSTRUCTION OF SPECIAL POINTS............................... 10 2. Tools........................................................................................................................................................ 10 3. Extension of open sets......................................................................................................................... 10 4. Construction of special points in X*................................................................................................... 12 CHAPTER II. EFFECTIVE PROOFS USING REMOTE POINTS................................................. 16 5. Remote points and extremal disconnectedness at points........................................................... 16 6. Remote points and nonhomogeneity................................................................................................ 17 7.Čech-Stone compactifications and products.................................................................................... 19 8. When "extremally disconnected at" implies remote....................................................................... 22 9. Far points, remote points, and nonhomogeneity............................................................................ 24 CHAPTER III. OTHER APPLICATIONS OF REMOTE POINTS................................................... 25 10. Two examples on extremal disconnectedness............................................................................ 25 11. A partition of R*.................................................................................................................................... 26 12. Extremal disconnectedness and C*-embedding......................................................................... 27 13. Connected compactifications........................................................................................................... 28 CHAPTER IV. PROPERTIES OF REMOTE POINTS.................................................................... 30 14: The structure of remote points.......................................................................................................... 30 15. Nonhomogeneity of spaces of special points............................................................................... 31 16. Special points and Baire spaces..................................................................................................... 32 17. Pseudocompact spaces between X and βX.................................................................................. 32 CHAPTER V. MISCELLANEOUS REMARKS................................................................................ 36 18. Zero-dimensional spaces................................................................................................................. 36 19. Q, Q*, Q**, Q***,................................................................................................................................... 37 20. Retractions from βX onto X*.............................................................................................................. 38 21. Products of remainders..................................................................................................................... 39 22. Questions............................................................................................................................................. 40 REFERENCES................................................................................................................................... 42 INDEX................................................................................................................................................... 44
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First countable and countable spaces all compactifications of which contain βN

60%
van Douwen E. K., Przymusiński T. C.
Fundamenta Mathematicae
|
1979
|
tom 102
|
nr 3
229-234
4
Content available remote

Cardinal functions on compact F-spaces and on weakly countably complete Boolean algebras

60%
van Douwen E. K.
Fundamenta Mathematicae
|
1981
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tom 114
|
nr 3
235-256
5
Content available remote

Separable extensions of first countable spaces

48%
van Douwen E. K., Przymusiński T. C.
Fundamenta Mathematicae
|
1979-1980
|
tom 105
|
nr 2
147-158
6
Content available remote

The box product of countably many metrizable spaces need not be normal

48%
van Douwen E. K.
Fundamenta Mathematicae
|
1975
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tom 88
|
nr 2
127-132
7
Content available remote

Small subsets of first countable spaces

43%
van Douwen E. K., Wage M. L.
Fundamenta Mathematicae
|
1979
|
tom 103
|
nr 2
103-110
8
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Homogeneity of βG if G is a topological group

42%
van Douwen E. K.
Colloquium Mathematicum
|
1979
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tom 41
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nr 2
193-199
9
Content available remote

Special bases for compact metrizable spaces

36%
van Douwen E. K.
Fundamenta Mathematicae
|
1981
|
tom 111
|
nr 3
201-209
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