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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction......................................................................................................................................... 5
Chapter I Elementary topological characterizations of fundamental dimension........................... 6
1. Characterizations of fundamental dimension..................................................................... 6
2. The fundamental dimension of components of compacta.............................................. 9
3. The fundamental dimension of the union of two compacta............................................. 10
Chapter II Cohomology groups over local systems and generalized local systems................... 13
1. Local systems of groups......................................................................................................... 13
2. Cohomology with coefficients in local systems.................................................................. 16
3. The Künneth formula
4. Generalized local systems..................................................................................................... 20
Chapter III Homological characterizations of fundamental dimension........................................... 22
1. Deformability of maps and the number................................................................................ 23
2. Obstructions to deformability.................................................................................................. 24
3. Coefficients of cyclicity and ℱ-continua................................................................................. 25
4. Continua with fundamental dimension ≥ 3........................................................................ 28
5. Two algebraic lemmas............................................................................................................ 29
6. Continua with fundamental dimension equal to 1............................................................. 31
7. Continua with fundamental dimension equal to 2............................................................. 33
8. The main results....................................................................................................................... 34
Chapter IV Applications of the homological characterizations of fundamental dimension
to the study of some special problems................................................................................................. 37
1. The fundamental dimension of the Cartesian product of a closed manifold
and a continuum........................................................................................................................................ 37
2. The fundamental dimension of the Cartesian product of a curve and a continuum... 38
3. An example of a finite-dimensional continuum with an infinite family of shape
factors and the fundamental dimension of the Cartesian product of polyhedra........................... 42
4. The fundamental dimension of the union of two compacta and of the quotient
space............................................................................................................................................................ 43
5. The fundamental dimension of the suspension of a compactum.................................. 44
6. The fundamental dimension of the Cartesian product of approximative
1-connected compacta............................................................................................................................. 46
7. The fundamental dimension of a subset of manifold....................................................... 48
Final remarks and problems................................................................................................................... 50
References.................................................................................................................................................. 52
Index of symbols........................................................................................................................................ 54
Introduction......................................................................................................................................... 5
Chapter I Elementary topological characterizations of fundamental dimension........................... 6
1. Characterizations of fundamental dimension..................................................................... 6
2. The fundamental dimension of components of compacta.............................................. 9
3. The fundamental dimension of the union of two compacta............................................. 10
Chapter II Cohomology groups over local systems and generalized local systems................... 13
1. Local systems of groups......................................................................................................... 13
2. Cohomology with coefficients in local systems.................................................................. 16
3. The Künneth formula
4. Generalized local systems..................................................................................................... 20
Chapter III Homological characterizations of fundamental dimension........................................... 22
1. Deformability of maps and the number................................................................................ 23
2. Obstructions to deformability.................................................................................................. 24
3. Coefficients of cyclicity and ℱ-continua................................................................................. 25
4. Continua with fundamental dimension ≥ 3........................................................................ 28
5. Two algebraic lemmas............................................................................................................ 29
6. Continua with fundamental dimension equal to 1............................................................. 31
7. Continua with fundamental dimension equal to 2............................................................. 33
8. The main results....................................................................................................................... 34
Chapter IV Applications of the homological characterizations of fundamental dimension
to the study of some special problems................................................................................................. 37
1. The fundamental dimension of the Cartesian product of a closed manifold
and a continuum........................................................................................................................................ 37
2. The fundamental dimension of the Cartesian product of a curve and a continuum... 38
3. An example of a finite-dimensional continuum with an infinite family of shape
factors and the fundamental dimension of the Cartesian product of polyhedra........................... 42
4. The fundamental dimension of the union of two compacta and of the quotient
space............................................................................................................................................................ 43
5. The fundamental dimension of the suspension of a compactum.................................. 44
6. The fundamental dimension of the Cartesian product of approximative
1-connected compacta............................................................................................................................. 46
7. The fundamental dimension of a subset of manifold....................................................... 48
Final remarks and problems................................................................................................................... 50
References.................................................................................................................................................. 52
Index of symbols........................................................................................................................................ 54
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
187
Liczba stron
54
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXVII
Daty
wydano
1981
Twórcy
autor
Bibliografia
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