Spaces of discrete shape and c-refinable maps that induce shape equivalences

M. A. MORÓN; F. R. Ruis Del PORTAL

doi:10.2969/jmsj/04940713

M. A. MORÓN, F. R. Ruis Del PORTAL

Author information

Keywords: shape, calmness, AWNR, c-refinable map

JOURNAL FREE ACCESS

1997 Volume 49 Issue 4 Pages 713-721

DOI https://doi.org/10.2969/jmsj/04940713

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Published: 1997 Received: August 22, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : M.A. MORÓN¹⁾, F.R. RUIZ Del PORTAL²⁾
Right : M. A. MORÓN¹⁾, F. R. Ruis Del PORTAL²⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) Unidad Docente de Matemáticas E.T.S.I. de Montes Universidad Politécnica de Madrid
2) Departmento de Geometría y Topología Facultad de CC. Matemáticas Universidad Complutense de Madrid

Right :
1) Unidad Docente de Matemáticas E. T. S. I. de Montes Universidad Politécnica de Madrid
2) Departmento de Geometría y Topología Facultad de CC. Matemáticas Universidad Complutense de Madrid

Date of correction: October 20, 2006 Reason for correction: - Correction: KEYWORD Details: Right : shape, calmness, AWNR, c-refinable map

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R.A. Alo and H.L. Shapiro, Normal topological spaces, Cambridge Univ. Press, 1974.
2) S.A. Bogatyi, Approximative and fundamental retracts, Math. USSR Sbornik, 22, 1 (1974), 91-103.
3) K. Borsuk, Theory of shape, Monografie Matematyczne, 59 (PWN, Warsaw, 1975).
4) Z. Cerin, Homotopy properties of locally compact spaces at infinity-calmness and smoothness, Pacific J. Math., 79, 1 (1978), 69-91.
5) Z. Cerin, Shape theory intrinsically, Publications Matemàtiques, 37 (1993), 317-334.
6) A. Dold, Lectures in algebraic topology, Springer-Verlag, Berlin, 1972.
7) J. Dydak and J. Segal, Shape theory: An Introduction, Lecture Notes in Math., 688 (Springer-Verlag, Berlin, 1978).
8) D.A. Edwards and R. Geoghegan, Compact weak equivalent to ANR's, Fund. Math., 90 (1975), 115-124.
9) D.A. Edwards and R. Geoghegan, Infinite-dimensional Whitehead and Vietoris theorems in shape and pro-homotopy, Trans. Amer. Math. Soc., 219 (1976), 351-360.
10) R. Geoghegan, Elementary proofs of stability theorems in pro-homotopy and shape, Gen. Top. Appl., 8 (1978), 265-281.
11) H. Kato, Refinable maps in the theory of shape, Fund. Math., 113 (1981), 119-129.
12) H. Kato, A remark on refinable maps and calmness, Proc. Amer. Math. Soc., 90, 4 (1984), 649-652.
13) A. Koyama, Refinable maps in dimension theory, Topology and its Appl., 17 (1984), 247-255.
14) K. Morita, The Hurewicz and the Whitehead theorems in shape theory, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, 12 (1974), 246-258.
15) M.A. Morón and F.R. Ruiz del Portal, Shape as a Cantor completion process, Math. Zeitschrift, 225, 1, (1997), 67-86.
16) M.A. Morón and F.R. Ruiz del Portal, A topology on the set of shape morphisms, preprint.
17) M.A. Morón and F.R. Ruiz del Portal, Counting shape and homotopy types among FANR's: An elementary approach, Manuscripta Math., 79 (1993), 411-414.
18) M.A. Morón and F.R. Ruiz del Portal, Ultrametrics and infinite-dimensional Whitehead theorems in shape theory, Manuscripta Math., 89 (1996), 325-333.
19) M.A. Morón and F.R. Ruiz del Portal, Multivalued maps and shape for paracompacta, Math. Japonica, 39, 3 (1994), 489-500.
20) S. Mardešic and J. Segal, Shape theory, North-Holland, Amsterdam, 1982.
21) R.H. Overton and J. Segal, A new construction of movable compacta, Glasnik Mat., 6 (1971), 361-363.
22) J.M.R. Sanjurjo, An intrinsic description of shape, Trans. Amer. Math. Soc., 329 (1992), 625-636.
23) W.H. Schikof, Ultrametric calculus: An introduction to p-adic analysis, Cambridge University Press, 1984.
24) E. Spanier, Algebraic Topology, McGraw-Hill, NY, 1966.
25) S. Spiez, A majorant for the class of movable compacta, Bull. Acad. Polon, Sci. Ser. Sci. Math. Astron. Phys., 21 (1973).
27) J.L. Taylor, A counterexample in shape theory, Bull. Amer. Math. Soc., 81, 3 (1975), 629-632.
27) K. Tsuda, On AWNR-spaces in shape theory, Math. Japonica, 22, 4 (1977), 471-478.

Right : [1] R. A. Alo and H. L. Shapiro, Normal topological spaces, Cambridge Univ. Press, 1974.
[2] S. A. Bogatyi, Approximative and fundamental retracts, Math. USSR Sbornik, 22, 1 (1974), 91-103.
[3] K. Borsuk, Theory of shape, Monografie Matematyczne, 59 (PWN, Warsaw, 1975).
[4] Z. Cerin, Homotopy properties of locally compact spaces at infinity-calmness and smoothness, Pacific J. Math., 79, 1 (1978), 69-91.
[5] Z. Cerin, Shape theory intrinsically, Publications Matemàtiques, 37 (1993), 317-334.
[6] A. Dold, Lectures in algebraic topology, Springer-Verlag, Berlin, 1972.
[7] J. Dydak and J. Segal, Shape theory: An Introduction, Lecture Notes in Math., 688 (Springer-Verlag, Berlin, 1978).
[8] D. A. Edwards and R. Geoghegan, Compact weak equivalent to ANR's, Fund. Math., 90 (1975), 115-124.
[9] D. A. Edwards and R. Geoghegan, Infinite-dimensional Whitehead and Vietoris theorems in shape and pro-homotopy, Trans. Amer. Math. Soc., 219 (1976), 351-360.
[10] R. Geoghegan, Elementary proofs of stability theorems in pro-homotopy and shape, Gen. Top. Appl., 8 (1978), 265-281.
[11] H. Kato, Refinable maps in the theory of shape, Fund. Math., 113 (1981), 119-129.
[12] H. Kato, A remark on refinable maps and calmness, Proc. Amer. Math. Soc., 90, 4 (1984), 649-652.
[13] A. Koyama, Refinable maps in dimension theory, Topology and its Appl., 17 (1984), 247-255.
[14] K. Morita, The Hurewicz and the Whitehead theorems in shape theory, Sci. Rep. Tokyo Kyoiku Daigaku, Sec. A, 12 (1974), 246-258.
[15] M. A. Morón and F. R. Ruiz del Portal, Shape as a Cantor completion process, Math. Zeitschrift, 225, 1, (1997), 67-86.
[16] M. A. Morón and F. R. Ruiz del Portal, A topology on the set of shape morphisms, preprint.
[17] M. A. Morón and F. R. Ruiz del Portal, Counting shape and homotopy types among FANR's: An elementary approach, Manuscripta Math., 79 (1993), 411-414.
[18] M. A. Morón and F. R. Ruiz del Portal, Ultrametrics and infinite-dimensional Whitehead theorems in shape theory, Manuscripta Math., 89 (1996), 325-333.
[19] M. A. Morón and F. R. Ruiz del Portal, Multivalued maps and shape for paracompacta, Math. Japonica, 39, 3 (1994), 489-500.
[20] S. Mardešic and J. Segal, Shape theory, North-Holland, Amsterdam, 1982.
[21] R. H. Overton and J. Segal, A new construction of movable compacta, Glasnik Mat., 6 (1971), 361-363.
[22] J. M. R. Sanjurjo, An intrinsic description of shape, Trans. Amer. Math. Soc., 329 (1992), 625-636.
[23] W. H. Schikof, Ultrametric calculus: An introduction to p-adic analysis, Cambridge University Press, 1984.
[24] E. Spanier, Algebraic Topology, McGraw-Hill, NY, 1966.
[25] S. Spiez, A majorant for the class of movable compacta, Bull. Acad. Polon, Sci. Ser. Sci. Math. Astron. Phys., 21 (1973).
[27] J. L. Taylor, A counterexample in shape theory, Bull. Amer. Math. Soc., 81, 3 (1975), 629-632.
[27] K. Tsuda, On AWNR-spaces in shape theory, Math. Japonica, 22, 4 (1977), 471-478.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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