Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Algebraic theory of fundamental dimension

Seria
Rozprawy Matematyczne tom/nr w serii: 187 wydano: 1981
Zawartość
Warianty tytułu
Abstrakty
EN
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
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
Bibliografia
  • [B1] K. Borsuk, Theory of Retracts, Warszawa 1967.
  • [B2] K. Borsuk, On several problems of the theory of shape. Studies in Topology (Proceedings of a Conference held at Charlote, North Carolina, March 14-16, 1974), Academic Press, Inc., New York 1975.
  • [B3] K. Borsuk, Theory of Shape, Warszawa 1975.
  • [C-Ch] J. H. Case and R. E. Chamberlin, Characterization of treelike compacta, Pacific J. Math. 10 (1960), pp. 73-84.
  • [D1] J. Dydak, A generalization of cohomotopy groups. Fund. Math. 90 (1975), pp. 77-98.
  • [D2] J. Dydak, On a paper by Y. Kodama, Bull. Acad. Polon. Sci. 25 (1977), p. 165.
  • [E-G] D. A. Edwards and R. Geoghegan, The stability problem in shape and a Whitehead theorem in pro-homotopy, Trans. Amer. Math. Soc. 214 (1975), pp. 261-277.
  • [H-S] D. Handel and J. Segal, An acyclic continuum with non-movable suspensions, Bull. Acad. Polon. Sci. 17 (1969), pp. 171-172.
  • [He] J. Hempel, 3-Manifolds, Ann. of Math. Stud. 86, Princeton 1976.
  • [Hi-Wy] P. J. Hilton and S. Wylie, Homology Theory, Cambridge 1960.
  • [Ho] W. Holsztyński, An extension and axiomatic characterization of the Borsuk's theory of shape, Fund. Math. 70 (1971), pp. 157-168.
  • [Hu1] Sze-Tsen Hu, Cohomology and deformation retracts, Proc. London Math. Soc. (2) 53 (1951), pp. 191-219.
  • [Hu2] Sze-Tsen Hu, Homotopy Theory, New York 1959.
  • [Hu3] Sze-Tsen Hu, Theory of Retracts. Detroit 1965.
  • [H-W] W. Hurewicz and H. Wallman, Dimension Theory, Princeton 1941.
  • [Ka] D. S. Kahn, An example in Čech cohomology, Proc. Amer. Math. Soc. 16 (1965), p. 584.
  • [Ko1] Y. Kodama, Cohomological dimension theory, Appendix to the book of K. Nagami "Dimension Theory", New York 1970.
  • [Ko2] Y. Kodama, On Δ -spaces and fundamental dimension in the sense of Borsuk, Fund. Math. 89 (1975), pp. 13-22.
  • [K] J. Keesling, Shape theory and compact connected abelian topological groups, Trans. Amer. Math. Soc. 194 (1974), pp. 349-358.
  • [Ku] V. I. Kuz'minov, liomological dimension theory (in Russian), Uspehi Mat. Nauk 23. 5 (143) (1968), pp. 3-49.
  • [L] J. Lambek, Lectures on Rings and Modules, London 1966.
  • [Ma] S. Mardešić, On the Whitehead theorem in shape theory I, Fund. Math. 91 (1976), pp. 51-64.
  • [M-S1] S. Mardešić and J. Segal, Shapes of compacta and ANR-systems, Fund. Math. 72 (1971), pp. 41-59.
  • [M-S2] S. Mardešić and J. Segal, Equivalence of the Borsuk and the ANR-sysfem approach to shapes. Fund. Math. 72 (1971), pp. 61-68.
  • [M-S3] S. Mardešić and J. Segal, Movable compacta and ANR-systems, Bull. Acad. Polon. Sci. 18 (1970), pp. 649-654.
  • [Mo] K. Morita, On shapes of topological spaces, Fund. Math. 86 (1975), pp. 251-259.
  • [N1] S. Nowak, Some properties of fundamental dimension, Fund. Math. 85 (1974), pp. 211-227.
  • [N2] S. Nowak, On the fundamental dimension of approximatively 1-compacta, Fund. Math. 89 (1975), pp. 61-79.
  • [N3] S. Nowak, An example of finite dimensional movable continuum with an infinite family of shape factors. Bull. Acad. Polon. Sci. 24 (1976), pp. 1019-1020.
  • [N4] S. Nowak, On the fundamental dimension of the Cartesian product of two compacta, Bull. Acad. Polon. Sci. 24 (1976), pp. 1021-1028.
  • [N5] S. Nowak, Some remarks concerning the fundamental dimension of the Cartesian product of two compacta, Fund. Math. 103 (1979), pp. 31-41.
  • [R-S] C. P. Rourke and B, J. Sanderson, Introduction to Piecewise-Linear Topology, New York 1972.
  • [P] L. S. Pontryagin, Continuous Groups (in Russian), Moscow 1973.
  • [S] E. Spanier, Algebraical Topology, New York 1966.
  • [Sp] S. Spież, On characterization of shapes of several compacta. Bull. Acad. Polon. Sci. 24 (1976), pp. 257-263.
  • [St1] N. E. Steenrod, Universal homology groups, Amer. J. Math. 58 (1936), pp. 661-701.
  • [St2] N. E. Steenrod, Homology with local coefficients, Ann. of Math. 44 (1943), pp. 610-627.
  • [St3] N. E. Steenrod, The Topology of Fibre Bundles, Princeton 1951.
  • [Sta] J. R. Stallings, On torsion-free groups with infinitely many ends, Ann. Math. 88 (1968), pp. 312-334.
  • [Sw] R. Swan, Groups of cohomological dimension "one", J. of Algebra 12 (1969), pp. 585-601.
  • [W] C. T. C. Wall, Finiteness conditions for CW complexes, Ann. of Math. 81 (1965), pp. 56-69.
  • [T1] Topology of 3-Manifolds, Proceedings of the University of Georgia Institute 1961, Prentice - Hall, Inc., Englewood Cliffs N. J., 1962.
  • [T2] Topology of Manifolds, Proceedings of the University, of Georgia Institute, Markhan Published Company, Chicago 1970.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-32308195-a9cd-40a9-bbf3-ac816424cc4f
Identyfikatory
ISBN
83-01-01250-1
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.