On the LC1-spaces which are Cantor or arcwise homogeneous
Patkowska, Hanna
Fundamenta Mathematicae, Tome 142 (1993), p. 139-146 / Harvested from The Polish Digital Mathematics Library
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A space X containing a Cantor set (an arc) is Cantor (arcwise) homogeneousiff for any two Cantor sets (arcs) A,B ⊂ X there is an autohomeomorphism h of X such that h(A)=B. It is proved that a continuum (an arcwise connected continuum) X such that either dim X=1 or X∈LC1 is Cantor (arcwise) homogeneous iff X is a closed manifold of dimension at most 2.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:211977 
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     year = {1993},
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Patkowska, Hanna. On the LC1-spaces which are Cantor or arcwise homogeneous. Fundamenta Mathematicae, Tome 142 (1993) pp. 139-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i2p139bwm/

[00000] [A] R. D. Anderson, A characterization of the universal curve and a proof of its homogeneity, Ann. of Math. 67 (1958), 313-324. | Zbl 0083.17607

[00001] [E] E. G. Effros, Transformation groups and C∞-algebras, ibid. 81 (1965), 38-55.

[00002] [Hu] S.-T. Hu, Theory of Retracts, Wayne St. Univ. Press, Detroit 1965. | Zbl 0145.43003

[00003] [L-W] J. Lamoreaux and D. G. Wright, Rigid sets in the Hilbert cube, Topology Appl. 22 (1986), 85-96. | Zbl 0587.54022

[00004] [M] J. van Mill, Infinite-Dimensional Topology, North-Holland, 1989. | Zbl 0663.57001

[00005] [O-P] K. Omiljanowski and H. Patkowska, On the continua which are Cantor homogeneous or arcwise homogeneous, Colloq. Math. 58 (1990), 201-212. | Zbl 0712.54024

[00006] [U] G. S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-400. | Zbl 0318.54037

[00007] [Wh1] G. T. Whyburn, Local separating points of continua, Monatsh. Math. Phys. 36 (1929), 305-314. | Zbl 55.0320.01

[00008] [Wh2] G. T. Whyburn, Concerning the proposition that every closed, compact and totally disconnected set of points is a subset of an arc, Fund. Math. 18 (1932), 47-60. | Zbl 58.0643.03

[00009] [Y] G. S. Young, Characterizations of 2-manifolds, Duke Math. J. 14 (1947), 979-990. | Zbl 0029.23204