Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Zapraszamy na https://bibliotekanauki.pl
Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Preface...................................................................................................................................... 5
I. Introduction............................................................................................................................ 7
II. Simple chains
2.1. Simplexes............................................................................................................ 12
2.2. Chains........................................................................................................................... 13
2.3. Boundary operator. Cycles and boundaries.......................................................... 15
2.4. Join operator................................................................................................................ 15
2.5. ε-simplexes and ε-chains........................................................................................... 16
III. Sequential chains
3.1. Sequences and subsequences...................................................................... 17
3.2. Sequential chains....................................................................................................... 18
3.3. Infinite chains. General homology groups............................................................. 18
3.4. Infinite chains in subspaces..................................................................................... 19
3.5. True cycles. Vietoris homology groups................................................................... 21
3.6. Subsequences of infinite chains............................................................................. 22
3.7. A condition for homology of infinite cycles.............................................................. 24
IV. Functions, mappings, and null translations
4.1. Homomorphisms of simple chains induced by functions...................................... 25
4.2. Homomorphisms of sequential chains induced by functions........................... 25
4.3. Homomorphisms of ε-chains induced by functions............................................ 26
4.4. Homomorphisms of infinite chains induced by maps........................................ 27
4.5. Topological invariance of the central and Vietoris homology groups............... 28
4.6. Non-equivalence of the general and Vietoris homology groups....................... 30
4.7. The homotopy theorem.............................................................................................. 31
4.8. Null translations.......................................................................................................... 34
V. The Phragmen-Brouwer theorem
5.1. Introduction.......................................................................................................... 37
5.2. The Phragmen Brouwer theorem for non-compact spaces............................... 39
VI. The Alexandroff dimension theorem
6.1. Introduction.......................................................................................................... 40
6.2. Compactly dimensioned spaces............................................................................. 41
6.3. The generalized Alexandroff theorem..................................................................... 43
Bibliography.............................................................................................................................. 46
Preface...................................................................................................................................... 5
I. Introduction............................................................................................................................ 7
II. Simple chains
2.1. Simplexes............................................................................................................ 12
2.2. Chains........................................................................................................................... 13
2.3. Boundary operator. Cycles and boundaries.......................................................... 15
2.4. Join operator................................................................................................................ 15
2.5. ε-simplexes and ε-chains........................................................................................... 16
III. Sequential chains
3.1. Sequences and subsequences...................................................................... 17
3.2. Sequential chains....................................................................................................... 18
3.3. Infinite chains. General homology groups............................................................. 18
3.4. Infinite chains in subspaces..................................................................................... 19
3.5. True cycles. Vietoris homology groups................................................................... 21
3.6. Subsequences of infinite chains............................................................................. 22
3.7. A condition for homology of infinite cycles.............................................................. 24
IV. Functions, mappings, and null translations
4.1. Homomorphisms of simple chains induced by functions...................................... 25
4.2. Homomorphisms of sequential chains induced by functions........................... 25
4.3. Homomorphisms of ε-chains induced by functions............................................ 26
4.4. Homomorphisms of infinite chains induced by maps........................................ 27
4.5. Topological invariance of the central and Vietoris homology groups............... 28
4.6. Non-equivalence of the general and Vietoris homology groups....................... 30
4.7. The homotopy theorem.............................................................................................. 31
4.8. Null translations.......................................................................................................... 34
V. The Phragmen-Brouwer theorem
5.1. Introduction.......................................................................................................... 37
5.2. The Phragmen Brouwer theorem for non-compact spaces............................... 39
VI. The Alexandroff dimension theorem
6.1. Introduction.......................................................................................................... 40
6.2. Compactly dimensioned spaces............................................................................. 41
6.3. The generalized Alexandroff theorem..................................................................... 43
Bibliography.............................................................................................................................. 46
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
180
Liczba stron
47
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXX
Daty
wydano
1980
Twórcy
autor
Bibliografia
- [1] P. S. Alexandroff, Untersuchungen über Gestalt und Luge abgeschlossener Mengen beliebiger Dimension, Ann. of Math. (2) 30 (1928), pp. 101-187.
- [2] P. S. Alexandroff, Dimensionstheorie. Ein Beitrag zur Geometrie der abgeschlossenen Mengen, Math. Ann, 106 (1932), pp. 161-238.
- [3] E. G. Begle, The Vietoris mapping theorem for bicompact spaces, Ann. of Math. 51 (1950), pp. 534-543.
- [4] R. H. Bing and K. Borsuk, Some remarks concerning topologically homogeneous spaces, ibidem 81 (1965), pp. 100-111.
- [5] K. Borsuk, Theory of retracts, Monografie Matematyczne 44, PWN - Polish Scientific Publishers, Warsaw 1967.
- [6] K. Borsuk, Topology of compacta, Lectures given at Rutgers University, New Brunswick, N. J., 1968 (Lecture notes, to appear).
- [7] K. Borsuk, and A. Kosiński, Families of acyclic compacta in euclidean n-space, Bull. Acad. Polon. Sci. (3) 3 (1955), pp. 293-296.
- [8] E. Čech, Théorie générale de l'homologie dans un espace quelconque, Fund. Math. 19 (1932), pp. 149-183.
- [9] J. Dugundji, Topology, Allyn and Bacon, Boston 1966.
- [10] S. Eilenberg, Sur quelques propriétés des transformations localement homéomorphes, Fund. Math. 24 (1935), pp. 35-42.
- [11] S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton University Press, Princeton, New Jersey 1952.
- [12] E. E. Floyd, The extension of homeomorphisms, Duke Math. J. 16 (1949), pp. 225-235.
- [13] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961.
- [14] W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press, Princeton, N, J., 1948.
- [15] J. L. Kelley, General topology, Van Nostrand, Princeton, N. J., 1955.
- [16] B. Knaster and C. Kuratowski, Sur les ensembles connexes, Fund, Math. 2 (1921), pp. 206-255.
- [17] A. Kosiński, On manifolds and r-spaces, ibidem 42 (1955), pp. 111-124.
- [18] S. Lefschetz, Topology, Amer. Math. Soc. Colloq. Publ. 12, New York 1930.
- [19] S. Lefschetz, Algebraic topology, ibid. 27, New York 1942.
- [20] S. Lefschetz, Topics in topology, Ann. of Math. Studies 10, Princeton University Press, Princeton, N. J., 1942.
- [21] Jun-iti Nagata, Modern dimension theory, North-Holland Publ. Co., Amsterdam 1965.
- [22] M. H. A. Newman, Local connection in locally compact spaces, Proc. Amer. Math. Soc. 1 (1950), pp. 44-53.
- [23] D. Rolfsen, Strongly convex metrices in cells. Bull, Amer. Math. Soc. 74 (1968), pp. 171-175.
- [24] D. Rolfsen, Characterizing the 3-cell by its metric, Fund. Math. 66 (1969), pp. 1-9.
- [25] S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957), pp. 604-610.
- [26] E. H. Spanier, Cohomology theory for general spaces, Ann. of Math. 49 (1948), pp. 407-427.
- [27] N. Steenrod, Regular cycles of compact metric spaces, ibidem 41 (1940), pp. 833-851.
- [28] L. Vietoris, Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann. 97 (1927), pp. 454-472.
- [29] G. T. Whyburn, Cyclic elements of higher orders, Amer. J. Math. 56 (1934), pp. 133-146.
- [30] G. T. Whyburn, The mapping of Betti groups under interior transformations, Duke Math. J. 4 (1938), pp. 1-8.
Języki publikacji
| EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-8f369e96-b1eb-4ec9-99e2-8c366367a5a4
Identyfikatory
ISBN
83-01-01116-5
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.