Limiting subcontinua and Whitney maps of tree-like continua

Hisao Kato

Compositio Mathematica (1988)

  • Volume: 66, Issue: 1, page 5-14
  • ISSN: 0010-437X

How to cite


Kato, Hisao. "Limiting subcontinua and Whitney maps of tree-like continua." Compositio Mathematica 66.1 (1988): 5-14. <>.

author = {Kato, Hisao},
journal = {Compositio Mathematica},
keywords = {tree-like continuum; Whitney map; absolute retract; Peano continuum; limiting subcontinuum},
language = {eng},
number = {1},
pages = {5-14},
publisher = {Kluwer Academic Publishers},
title = {Limiting subcontinua and Whitney maps of tree-like continua},
url = {},
volume = {66},
year = {1988},

AU - Kato, Hisao
TI - Limiting subcontinua and Whitney maps of tree-like continua
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 66
IS - 1
SP - 5
EP - 14
LA - eng
KW - tree-like continuum; Whitney map; absolute retract; Peano continuum; limiting subcontinuum
UR -
ER -


  1. 1 K. Borsuk: Theory of Shape, Monografie Mathematyczne59, Warszawa (1975). Zbl0317.55006MR418088
  2. 2 K. Borsuk: Theory of Retracts, Monografie Mathematyczne44, Warszawa (1967). Zbl0153.52905MR216473
  3. 3 S.T. Hu: Theory of Retracts, Wayne State Univ. Press, Detroit (1965). Zbl0145.43003MR181977
  4. 4 H. Kato: Concerning hyperspaces of certain Peano continua and strong regularity of Whitney maps, Pacific J. Math.119 (1985) 159-167. Zbl0524.55015MR797021
  5. 5 H. Kato: Shape properties of Whitney maps for hyperspaces, Trans. Amer. Math. Soc.297 (1986) 529-546. Zbl0607.54014MR854083
  6. 6 H. Kato: Whitney continua of curves, Trans. Amer. Math. Soc.300 (1987) 367-381. Zbl0621.54006MR871681
  7. 7 H. Kato: Whitney continua of graphs admit all homotopy types of compact connected ANRs, Fund. Math. (to appear). Zbl0652.55013MR962537
  8. 8 H. Kato: Various types of Whitney maps on n-dimensional compact connected polyhedra (n ≽ 2), Topology Appl. (to appear). Zbl0631.54004
  9. 9 H. Kato: Movability and homotopy, homology pro-groups of Whitney continua, J. Math. Soc. Japan39 (1987) 435-446. Zbl0608.54003MR900978
  10. 10 H. Kato: On admissible Whitney maps, Colloq. Math. (to appear). Zbl0703.54009MR991218
  11. 11 H. Kato: Shape equivalences of Whitney continua of curves, Canad. J. Math. (to appear). Zbl0628.54010MR928220
  12. 12 H. Kato: On local 1-connectedness of Whitney continua, Fund. Math. (to appear). Zbl0675.54032MR978718
  13. 13 J.L. Kelley: Hyperspaces of a continuum, Trans. Amer. Math. Soc.52 (1942) 22-36. Zbl0061.40107MR6505
  14. 14 J. Krasinkiewicz: On the hyperspaces of snake-like and circle-like continua, Fund. Math.83 (1974) 155-164. Zbl0271.54024MR418058
  15. 15 J. Krasinkiewicz and S.B. Nadler, Jr.: Whitney properties, Fund. Math.98 (1978) 165-180. Zbl0376.54013MR467691
  16. 16 J. Leray: Theorie des points fixes: indice total et nombre de Lefschetz, Bull. Soc. Math. France87 (1959) 221-233. Zbl0093.36702MR143202
  17. 17 M. Lynch: Whitney properties for 1-dimensional continua, Bull. Acad. Polon. Sci. (to appear). Zbl0637.54028MR939010
  18. 18 S.B. Nadler, Jr.: Hyperspaces of sets, Pure and Appl. Math. Dekker, New York (1978). Zbl0432.54007MR500811
  19. 19 A. Petrus: Contractibility of Whitney continua in C(X), Gen. Topology Appl.9 (1978) 275-288. Zbl0405.54006MR510909
  20. 20 J.T. Rogers, Jr.: Whitney continua in the hyperspace C(X), Pacific J. Math.58 (1975) 569-584. Zbl0322.54016MR383372
  21. 21 H. Whitney: Regular families of curves I, Proc. Nat. Acad. Sci. U.S.A.18 (1932) 275-278. Zbl0004.07503JFM58.0633.02
  22. 22 M. Wojdyslawski: Rétractes absolus et hyperespaces des continus, Fund. Math.32 (1939) 184-192. Zbl0021.36001JFM65.0880.03

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