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Tytuł książki

Strong shape theory

Autorzy

J. Dydak J. Segal

Seria

Rozprawy Matematyczne tom/nr w serii: 192 wydano: 1981

Zawartość

Pełne teksty:
rm192_01.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS

1. Introduction..................................................................................................................................... 5
2. Terminology and notation.................................................................................................................... 6
3. Proper maps on contractible telescopes.......................................................................................... 8
4. The strong shape category.................................................................................................................. 13
5. Semi-equivalences............................................................................................................................... 19
6. Geometric characterization of maps inducing strong shape equivalences............................... 21
7. Some classes of maps which induce strong shape equivalence............................................... 27
8. Concluding remarks............................................................................................................................. 35
References.................................................................................................................................................. 38

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 192

Liczba stron

39

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CXCII

Daty

wydano
1981

Twórcy

autor
J. Dydak
autor
J. Segal

Bibliografia

  • [B1] K. Borsuk, Concerning homotopy properties of compacta, Fund. Math. 62 (1968), pp. 223-254,
  • [B2] K. Borsuk, Theory of Shape, Warszawa 1975.
  • [B3] K. Borsuk, Theory of Retracts, Warszawa 1967.
  • [B-S] B. J. Ball and R. S her, A theory of proper shape for locally compact metric spaces, Fund, Math. 86 (1974), pp. 163-192.
  • [C-H] A. Calder and H. M. Hastings, Realizing Strong Shape Equivalences, preprint.
  • [C1] T. A. Chapman, Lectures on Hilbert cube manifolds. Lectures of the CBMS, No. 28 (1976).
  • [C2] T. A. Chapman, On some applications of infinite-dimensional manifolds to the theory of shape, Fund. Math. 76 (1972), pp. 181-193.
  • [C-S] T. A. Chapman and L. C. Siebenmann, Finding a boundary for a Hilbert cube manifolds. Acta Math. 137 (1976), pp. 171-208.
  • [D1] J. Dydak, Some remarks on the shape of decomposition spaces, Bull. Acad. Polon. Sci. Sér. Sci, Math. Astronom. Phis. 23 (1975), pp. 561-563.
  • [D2] J. Dydak, Movability and the shape of the decomposition spaces, ibidem, pp. 447-452.
  • [D3] J. Dydak, Some remarks concerning the Whitehead theorem in shape theory, ibidem, pp. 437-446.
  • [D4] J. Dydak, On a paper by Y. Kodama, ibidem, 25 (1977), pp. 163-174.
  • [D5] J. Dydak, A simple proof that pointed FANR-spaces are regular fundamental retracts of ANR's, ibidem, pp. 55-62.
  • [D6] J. Dydak, On unions of movable spaces, ibidem, 26 (1978), pp. 57-60.
  • [D7] J. Dydak, Pointed and unpointed shape and pro-homotopy. Fund. Math. 107 (1979), pp. 57-69.
  • [D8] J. Dydak, The Whitehead and Smale theorems in shape theory, Dissertationes Math. 156 (1979), pp. 1-55.
  • [D-O] J. Dydak, and M. Orlowski, On the sum of FANR-spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), pp. 165-167,
  • [D-K-P] Tom Dieck, K. H. Kamps and D. Puppe, Homotopietheorie, Lecture Notes in Math. No. 157 (1970).
  • [E-G1] D. A. Edwards and R. Geoghegan, Infinite-dimensional Whitehead and Vietoris theorems in shape and pro-homotopy. Trans, Amer. Math. Soc. 219 (1976), pp. 351-360.
  • [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-H1] D. A. Edwards and H. M. Hastings, Every weak proper homotopy equivalence is weakly properly homotopic to a proper homotopy equivalence. Trans. Amer. Math. Soc. 221 (1976), pp. 239-248.
  • [E-H2] D. A. Edwards and H. M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Math. No. 542 (1976).
  • [G] R. Geoghegan, A note on the vanishing of $lim^1$, J. Pure and Appl. Algebra 17 (1980), pp. 113-116.
  • [H] H. M. Hastings, Steenrod homotopy theory, homotopy idempotents, and homotopy limits. Topology Proceedings 2 (1977), pp. 461-477. LSU, Baton Rouge, March 1977.
  • [Kod1] Y. Kodama, On Δ-spaces and fundamental dimension in the sense of Borsuk, Fund. Math. 89 (1975), pp. 13-22.
  • [Kod2] Y. Kodama, On fine n-movability, J. Math. Soc. Japan 30 (1978), pp. 101-116.
  • [K-O1] Y. Kodama and Y. Ono, On fine shape theory I, Fund. Math. 105 (1979), pp. 29-39.
  • [K-O2] Y. Kodama and Y. Ono, On fine shape theory II, Fund. Math. 108 (1980), pp. 89-98..
  • [K] G. Kozłowski, Images of ANR's, to appear in Trans. Amer. Math. Soc.
  • [K-S] G. Kozłowski and J. Segal, Locally well-behaved paracompact in shape theory, Fund. Math. 95 (1977), pp. 55-71.
  • [K-M] J. Krasinkiewicz and P. Mine, Generalized paths and pointed 1-movability, Fund. Math. 104 (1979), pp. 141-153.
  • [M1] S. Mardešić, Shapes for topological spaces, Gen. Top. and Appl. 3 (1973), pp. 265-282.
  • [M2] S. Mardešić Pairs of compacta and trivial shape. Trans. Amer. Math. Soc. 189 (1974), pp. 329-336.
  • [M-S1] S. Mardešić and J. Segal, Shapes of compacta and AKK-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. Ser. Sci. Math. Astronom. Phys. 18 (1970), pp. 649-654.
  • [Mor] K. Morita, The Hurewicz and the Whitehead theorems in shape theory, Sci. Rep. of the Tokyo Kyoiku Daigaku, Sec. A, vol. 12 (1974), pp. 246-258.
  • [Mos1] M. Moszyńska, Concerning the Whitehead theorem for movable compacta, Fund. Math. 92 (1976), pp. 43-55.
  • [Mos2] M. Moszyńska, On shape and fundamental deformation retracts I, Fund. Math. 75 (1972), pp. 145-167.
  • [Mos3] M. Moszyńska, On shape and fundamental deformation retracts II, Fund. Math. 77 (1973), pp. 235-240.
  • [Mos4] M. Moszyńska, The Whitehead Theorem in the theory of shapes, Fund. Math. 80 (1973), pp. 221-263.
  • [N] S. Nowak, Some properties of the fundamental dimension, Fund. Math. 85 (1974), pp. 211-227.
  • [Or] M. Orłowski, On fundamental matching of compacta II and III, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 25 (1977), pp. 1149-1158.
  • [Seg] J. Segal, Lecture notes in shape theory, mimeographed notes, University of Washington, 1976.
  • [Sh] R. B. Sher, Extensions, retracts, and absolute neighborhood retract in proper shape theory. Fund. Math. 96 (1977), pp. 149-159.
  • [S1] L. C. Siebenmann, Infinite simple homotopy types, Indag. Math, 32 (1970), pp. 479-495.
  • [S2] L. C. Siebenmann, Chapman's classification of shapes: A proof using collapsing, Manuscripta Math. 16 (1975), pp. 373-384.
  • [S3] L. C. Siebenmann, Regular (or canonical) open neighborhoods, Gen. Top. and Appl. 3 (1973), pp. 51-62.
  • [S-W] E. H. Spanier and J. H. C. Whitehead, Obstructions to compression. Quart. J. Math. 6 (1955), pp. 91-105.
  • [Spa] E. H. Spanier Algebraic Topology, New York 1966.

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EN

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Identyfikator YADDA

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ISBN
83-01-01254-4
ISSN
0012-3862

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DML-PL
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