Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

The Whitehead and the Smale theorems in shape theory

Autorzy

Jerzy Dydak

Seria

Rozprawy Matematyczne tom/nr w serii: 156 wydano: 1978

Zawartość

Pełne teksty:
rm156_01.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS

§1. Introduction................................................................................................................................... 5
§2. Some classes of objects and morphisms in pro-categories..................................................... 5
§3. Shape category.................................................................................................................................... 14
§4. Deformation dimension..................................................................................................................... 16
§5. Some properties of n-equivalences of pro-$H_0$ ...................................................................... 18
§6. The Whitehead theorems in shape and pro-homotopy.............................................................. 26
§7. Criteria for stability in shape and pro-homotopy........................................................................... 29
§8. The Smale theorem in shape theory............................................................................................... 37
References.................................................................................................................................................. 49

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 156

Liczba stron

51

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CLVI

Daty

wydano
1978

Twórcy

autor
Jerzy Dydak
  • Institute of Mathematics, University of Warsaw

Bibliografia

  • [A-M] M. Artin and B. Mazur, Etale homotopy, Lecture Notes in Math. No. 100, Springer, Berlin 1969.
  • [A-S] M. F. Atyiah and G. B. Segal, Equivariant K-theory and completion, J. Diff. Geometry 3 (1969), pp. 1-18.
  • [Bog1] S. Bogatyi, On Vietoris problem for shapes, inverse limits and one Iu. M. Smirnov's problem, Dokl. Akad. Nauk SSSB 211 (1973), pp. 764-767.
  • [Bog2] S. Bogatyi, On Vietoris theorem in homotopy category and on Borsuk's problem, Fund. Math. 84 (1974), pp. 208-228.
  • [Bog3] S. Bogatyi, On the conservation of shapes in mappings, Dokl. Akad. Nauk SSSR 224 (1976), pp. 261-264.
  • [Ban] S. Banach, Über metrische Gruppen, Studia Math. 3 (1931), pp. 101-113.
  • [Bor1] K. Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), pp. 223-254.
  • [Bor2] K. Borsuk, Concerning the notion of shape for compacta, Proc. Int. Symp. on Topology and its Applications, Herceg Novi 1969, pp. 98-104.
  • [Bor3] K. Borsuk, Theory of retracts, Monografie Matematyczne 44, Warszawa 1967.
  • [Bor4] K. Borsuk, On movable compacta. Fund. Math. 66 (1969), pp. 137-146.
  • [Bor5] K. Borsuk, Theory of shape, Monografie Matematyczne 69, Warszawa 1976.
  • [Bore] K. Borsuk, Some remarks on shape properties of compacta, Fund. Math. 85 (1974), pp. 185-195.
  • [B-K] A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. No. 304, Springer, Berlin 1972.
  • [Br] E. H. Brown, Abstract homotopy theory, Trans. Amer. Math. Soc. 119 (1965), pp. 79-85.
  • [Dem] L. Demers, On spaces which have the shape of CW complexes, Fund. Math. 90 (1975), pp. 1-9.
  • [D-K] J. Draper and J. Keesling, An example concerning the Whitehead theorem in shape theory, ibid. 92 (1976), pp. 255 — 259.
  • [Dyd1] J. Dydak, A generalization of cohomotopy groups, ibid. 90 (1975), pp. 77-98.
  • [Dyd2] J. Dydak, On the shape of decomposition spaces, Bull. Acad. Polon. Sci. 23 (1975), pp. 293-298.
  • [Dyd3] J. Dydak, Movability and the shape of decomposition spaces, ibid. 23 (1976), pp. 447-452.
  • [Dyd4] J. Dydak, Some remarks concerning the Whitehead theorem in shape theory, ibid. .23 (1975), pp. 437-446.
  • [Dyd5] J. Dydak, Some remarks on the shape of decomposition spates, ibid. 23 (1975), pp. 561-563.
  • [Dyd6] J. Dydak, On the Whitehead theorem in pro-homotopy and on question of Mardesic, ibid. 23 (1975), pp. 775-779.
  • [Dyd7] J. Dydak, On a conjecture of Edwards, ibid. 23 (1975), pp. 771-774.
  • [Dyd8] J. Dydak, An algebraic condition characterizing FANR-spaces, ibid. 24 (1976), pp. 501-504.
  • [Dyd9] J. Dydak, On the Whitehead theorem, in shape theory. Thesis (Polish), Warsaw 1975.
  • [Dyd10] J. Dydak, Concerning the abelization of the first shape group of pointed continua, Bull. Acad. Polon. Sci. 24 (1976), pp. 615-620
  • [Dyd11] J. Dydak, A simple proof that pointed connected FANR-spaces are regular fundamental retracts of ANR’s, ibid. 25 (1977), pp. 55-62.
  • [Dug] J. Dugundji, Modified Vietoris theorems for homotopy, Fund. Math. 66 (1970), pp. 223-235.
  • [E-G1] D. A. Edwards and R. Geoghegan, Compacta weak shape equivalent to ANR's, ibid. 90 (1976), pp. 115-124.
  • [E-G2] 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.
  • [E-G3] D. A. Edwards and R. Geoghegan, Infinite-dimensional Whitehead and Vietoris theorems in shape and pro-homotopy, ibid. 219 (1976), pp. 351-360.
  • [E-G4] D. A. Edwards and R. Geoghegan, Shapes of complexes, ends of manifolds and the Wall obstruction, Ann. Math. 10 (1975), pp. 621-535.
  • [E-G5] D. A. Edwards and R. Geoghegan, Stability theorems in shape and pro-homotopy, Trans. Amer. Math. Soc. 222 (1976), pp. 384-401.
  • [E-H1] D. A. Edwards and H. M. Hastings, Counterexamples to infinitedimensional Whitehead theorems in prohomotopy, preprint.
  • [E-H2] D. A. Edwards and H. M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes 542, Springer, 1976.
  • [Edw] D. A. Edwards, Etale homotopy theory and shape, Pro. Conf. on Alg. Top., SUNY, Binghamton 1973, Lecture Notes in Math. 428 Springer, 1974, pp. 58-107.
  • [Fox] R. H. Fox, On shape, Fund. Math. 74 (1972), pp. 47-71.
  • [G] R. Geoghean, Elementary proofs of stability theorems in pro-homotopy and shape, Gen. Top. and its Appl. 8 (1978), pp. 265-281.
  • [G-L] R. Geoghegan and R. C. Lâcher, Compacta with the shape of finite complexes, Fund. Math. 92 (1976), pp. 25-27.
  • [Groth] A. Grothendieck, Technique de descente et théorèms d'existence en géométrie algébraique II, Sem. Bourbaki, 12 année, 1959-1960, Exp. 195, pp. 1-22.
  • [Hu] S. T. Hu, Theory of retracts, Wayne State Univ. Press, 1965.
  • [K1] J. Keesling, On the Whitehead theorem in shape theory, Fund. Math. 92 (1976), pp. 247-253.
  • [K2] J. Keesling, A trivial-shape décomposition of the Hilbert cube such that the decomposition space is not an AR, Bull. Acad. Polon. Sci. 23 (1975), pp. 997-998.
  • [Kod1] Y. Kodama, On the shape of decomposition spaces, J. Math. Soq. Japan 26 (1974), pp. 635-645.
  • [Kod2] Y. Kodama, Decomposition spaces and the shape in the sense of Fox, Fund. Math. 97 (1977), pp. 199-208.
  • [Koz] G. Kozlowski, Factorization of certain maps up to homotopy, Proc. Amer. Math. Soc. 21 (1969), pp. 88-92.
  • [K-S1] G. Kozlowski and J. Segal, Movability and shape connectivity, Fund. Math. 93 (1976), pp. 145-154.
  • [K-S2] G. Kozlowski and J. Segal, Local behavior and the Vietoris and Whitehead theorems in shape theory, ibid. (to appear).
  • [Kup] K. Kuperberg, Two Vietoris-type isomorphism theorems in Borsuk's theory of shape concerning the Vietoris-Čech homology and Borsuk's fundamental groups, Studies in Topology Charlotte Conference 1974, Academic Press, 1975, pp. 285-314. [Kur] K. Kuratowski, Topology, vol. I, Academic Press, 1966.
  • [La1] R. C. Lacher, Cell-like mappings I, Pacific J. Math. 30 (1969), pp. 717-731.
  • [La2] R. C. Lacher, Cell-like mappings II, ibid. 35 (1970), pp. 649-660.
  • [La3] R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), pp. 495-522.
  • [L-W] A. T. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand 1969.
  • [ML] S. MacLane, Categories for the working mathematician. Springer Verlag, 1971.
  • [Mar1] S. Mardešić, Shapes for topological spaces, Gen. Top. and its Appl. 3 (1973), pp. 265-282.
  • [Mar2] S. Mardešić, On the Whitehead theorem in shape theory, I, Fund. Math. 91 (1976), pp. 51-64.
  • [Mar3] S. Mardešić, On the Whitehead theorem in shape theory, II, ibid. 91 (1976), pp. 93-103. [M-S] S. Mardešić and J. Segal, Movable compacta and ANR-systems, Bull. Acad. Polon. Sci. 18 (1970), pp. 649-654.
  • [Mor1] K. Morita, Čech cohomology and covering dimension for topological spaces, Fund. Math. 87 (1975), pp. 31-52.
  • [Mor2] K. Morita, On shapes of topological spaces, ibid. 86 (1975), pp. 261-259.
  • [Mor3] K. Morita, The Eurewicz and the Whitehead theorems in shape theory, Sc. Rep. of the Kyoiku Daigaku 12 (1974), pp. 246-258.
  • [Mor4] K. Morita, Another form of the Whitehead theorem in shape theory, Proc. Japan Acad. 51 (1975), pp. 394^398.
  • [Mor6] K. Morita, A Vietoris theorem in shape theory, ibid. 61 (1975), pp. 696-701. [Mos-J M. Moszyńska, Uniformly movable compact spaces and their algebraic properties, Fund. Math. 77 (1972), pp. 126-144.
  • [Mos2] K. Morita, The Whitehead theorem in the theory of shapes, ibid. 80 (1973), pp. 221-263.
  • [MoSg] K. Morita, The Whitehead theorem for uniformly movable topological spaces, Bull. Acad. Polon. Sci. 23 (1975), pp. 993-996.
  • [Mos4] K. Morita, Concerning the Whitehead theorem for movable compacta, Fund. Math. 92 (1976), pp. 43-55.
  • [Mos5] K. Morita, Various approaches to the fundamental groups, ibid. 78 (1973), pp. 107-118.
  • [Now] S. Nowak, Some properties of fundamental dimension, ibid. 86 (1974), pp. 211-227.
  • [Sh] R. B. Sher, Realizing cell-like maps in Euclidean space, Gen. Top. and its Appl. 3 (1973), pp. 75-87.
  • [Sm] S. Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1967), pp. 604-610.
  • [S] E. Spanier, Algebraic topology, New York 1966.
  • [S-W] E. Spanier and J. H. C. Whitehead, Obstructions to compression, Quart. J. Math. 6 (1955), pp. 91-105.
  • [Sp] S. Spież, Movability and uniform movability, Bull. Acad. Polon. Sci. 22 (1974), pp. 43—45.
  • [Tay] J. L. Taylor, A counterexample in shape theory, Bull. Amer. Math. Soc. 81 (1976), pp. 629-632.
  • [Wat] C. T. C. Wall, Finiteness conditions for CW complexes, Ann. of Math. 81 (1965), pp. 55-69.
  • [Wat] T. Watanabe, On Cech homology and a stability theorem in shape theory, J. Math. Soc. Japan 29 (1977), pp. 655-664.
  • [Wh] J. H. C. Whitehead, Combinatorial homotopy I, Bull. Amer. Math. Soc. 65 (1949), pp. 213-245.

Języki publikacji

EN

Uwagi

Identyfikator YADDA

bwmeta1.element.zamlynska-1101479d-6651-42f5-82a0-1b46844a50b8

Identyfikatory

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.