A note on fundamental dimensions of Whitney continua of graphs

Hisao KATO

doi:10.2969/jmsj/04120243

Hisao KATO

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 2 Pages 243-250

DOI https://doi.org/10.2969/jmsj/04120243

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Published: 1989 Received: September 28, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) K. Borsuk, Theory of shape, Monograf. Mat., 59, PWN, Warszawa, 1975.
2) R. Duda, On the hyperspace of subcontinua of a finite graph, I, II, Fund. Math., 62 (1968), 265-286; 63 (1968), 225-255.
3) R. Duda, Correction to the paper “On the hyperspace of subcontinua of a finite graph, I”. Fund. Math., 69 (1970), 207-211.
4) H. Kato, Shape properties of Whitney maps for hyperspaces, Trans. Amer. Math. Soc., 297 (1986), 529-546.
5) H. Kato, Whitney continua of curves, Trans. Amer. Math. Soc., 300 (1987), 367-381.
6) H. Kato, Movability and homotopy, homology pro-groups of Whitney continua, J. Math. Soc. Japan, 39 (1987), 435-446.
7) H. Kato, Whitney continua of graphs admit all homotopy types of compact connected ANR's, Fund. Math., 129 (1988), 161-166.
8) H. Kato, Various types of Whitney maps on n-dimensional compact connected polyhedra (n_??_2), Topology Appl., 28 (1988), 17-21.
9) H. Kato, Shape equivalences of Whitney continua of curves, Canad. J. Math., 40 (1988), 217-227.
10) H. Kato, Limiting subcontinua and Whitney maps of tree-like continua, Compositio Math., 66 (1988), 5-14.
11) J.L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc., 52 (1942), 22-36.
12) J. Krasinkiewicz, Shape properties of hyperspaces, Fund. Math., 101 (1978), 79-91.
13) J. Krasinkiewicz and S. B. Nadler, Jr., Whitney properties, Fund. Math., 98 (1978), 165-180.
14) M. Lynch, Whitney levels in C_p(X) are absolute retracts, Proc. Amer. Math. Soc., 97 (1986), 748-750.
15) M. Lynch, Whitney properties of 1-dimensional continua, Bull. Acad. Polon. Sci., 35 (1987), 473-478.
16) S. Mardešic and J. Segal, Shape theory, North-Holland Mathematical Library, 1982.
17) S. B. Nadler, Jr., Hyperspaces of sets, Pure and Appl. Math., 49, Dekker, New York, 1978.
18) S. Nowak, Some properties of fundamental dimension, Fund. Math., 85 (1974), 211-227.
19) A. Petrus, Contractibility of Whitney continua in C(X), General Topology Appl., 9 (1978), 275-288.
20) J. T. Rogers, Jr., Applications of Vietoris-Begle theorem for multi-valued maps to the cohomology of hyperspaces, Michigan Math. J., 22 (1975), 315-319.
21) J. T. Rogers, Jr., Dimension and Whitney subcontinua of C(X), General Topology Appl., 6 (1976), 91-100.
22) H. Whitney, Regular families of curves I, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 275-278.

Right : [1] K. Borsuk, Theory of shape, Monograf. Mat., 59, PWN, Warszawa, 1975.
[2] R. Duda, On the hyperspace of subcontinua of a finite graph, I, II, Fund. Math., 62 (1968), 265-286; 63 (1968), 225-255.
[3] R. Duda, Correction to the paper “On the hyperspace of subcontinua of a finite graph, I”. Fund. Math., 69 (1970), 207-211.
[4] H. Kato, Shape properties of Whitney maps for hyperspaces, Trans. Amer. Math. Soc., 297 (1986), 529-546.
[5] H. Kato, Whitney continua of curves, Trans. Amer. Math. Soc., 300 (1987), 367-381.
[6] H. Kato, Movability and homotopy, homology pro-groups of Whitney continua, J. Math. Soc. Japan, 39 (1987), 435-446.
[7] H. Kato, Whitney continua of graphs admit all homotopy types of compact connected ANR's, Fund. Math., 129 (1988), 161-166.
[8] H. Kato, Various types of Whitney maps on n-dimensional compact connected polyhedra (n≥2), Topology Appl., 28 (1988), 17-21.
[9] H. Kato, Shape equivalences of Whitney continua of curves, Canad. J. Math., 40 (1988), 217-227.
[10] H. Kato, Limiting subcontinua and Whitney maps of tree-like continua, Compositio Math., 66 (1988), 5-14.
[11] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc., 52 (1942), 22-36.
[12] J. Krasinkiewicz, Shape properties of hyperspaces, Fund. Math., 101 (1978), 79-91.
[13] J. Krasinkiewicz and S. B. Nadler, Jr., Whitney properties, Fund. Math., 98 (1978), 165-180.
[14] M. Lynch, Whitney levels in C_p(X) are absolute retracts, Proc. Amer. Math. Soc., 97 (1986), 748-750.
[15] M. Lynch, Whitney properties of 1-dimensional continua, Bull. Acad. Polon. Sci., 35 (1987), 473-478.
[16] S. Mardešic and J. Segal, Shape theory, North-Holland Mathematical Library, 1982.
[17] S. B. Nadler, Jr., Hyperspaces of sets, Pure and Appl. Math., 49, Dekker, New York, 1978.
[18] S. Nowak, Some properties of fundamental dimension, Fund. Math., 85 (1974), 211-227.
[19] A. Petrus, Contractibility of Whitney continua in C(X), General Topology Appl., 9 (1978), 275-288.
[20] J. T. Rogers, Jr., Applications of Vietoris-Begle theorem for multi-valued maps to the cohomology of hyperspaces, Michigan Math. J., 22 (1975), 315-319.
[21] J. T. Rogers, Jr., Dimension and Whitney subcontinua of C(X), General Topology Appl., 6 (1976), 91-100.
[22] H. Whitney, Regular families of curves I, Proc. Nat. Acad. Sci. U. S. A., 18 (1932), 275-278.

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