On dimensions of non-Hausdorff sets for plane homeomorphisms

Hiromichi NAKAYAMA

doi:10.2969/jmsj/04740789

Hiromichi NAKAYAMA

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JOURNAL FREE ACCESS

1995 Volume 47 Issue 4 Pages 789-793

DOI https://doi.org/10.2969/jmsj/04740789

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Published: 1995 Received: January 27, 1994 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) L. E. J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54.
2) M. Brown, A new proof of Brouwer's lemma on translation arcs, Houston J. Math., 10(1984), 35-41.
3) M. Brown, Homeomorphisms of two-dimensional manifolds, Houston J. Math., 11 (1985), 455-469.
4) M. Brown, Fundamental regions of planar homeomorphisms, Contemp. Math., 117 (1991), 49-56.
5) A. Fathi, An orbit closing proof of Brouwer's lemma on translation arcs, Enseign. Math., 33 (1987), 315-322.
6) L. Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, preprint.
7) A. Haefliger and G. Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseign. Math., 3 (1957), 107-126.
8) W. Hurewicz and H. Wallman, Dimension Theory, Princeton Univ. Press, Princeton, N.J., 1948.
9) B. de Kerékjártó, Sur le groupe des transformations topologiques du plan, Ann. Scuola Norm. Sup. Pisa CI. Sci., (1934), 393-400.
10) B. de Kerékjártó, Über die fixpunktfreien Abbildungen der Ebene, Acta Sci. Math. (Szeged), 6 (1934), 226-234.
11) S. Matsumoto, Flows of the solid torus and fixed point free homeomorphisms of the plane, unpublished.

Right : [1] L. E. J. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54.
[2] M. Brown, A new proof of Brouwer's lemma on translation arcs, Houston J. Math., 10 (1984), 35-41.
[3] M. Brown, Homeomorphisms of two-dimensional manifolds, Houston J. Math., 11 (1985), 455-469.
[4] M. Brown, Fundamental regions of planar homeomorphisms, Contemp. Math., 117 (1991), 49-56.
[5] A. Fathi, An orbit closing proof of Brouwer's lemma on translation arcs, Enseign. Math., 33 (1987), 315-322.
[6] L. Guillou, Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, preprint.
[7] A. Haefliger and G. Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseign. Math., 3 (1957), 107-126.
[8] W. Hurewicz and H. Wallman, Dimension Theory, Princeton Univ. Press, Princeton, N. J., 1948.
[9] B. de Kerékjártó, Sur le groupe des transformations topologiques du plan, Ann. Scuola Norm. Sup. Pisa CI. Sci., (1934), 393-400.
[10] B. de Kerékjártó, Über die fixpunktfreien Abbildungen der Ebene, Acta Sci. Math. (Szeged), 6 (1934), 226-234.
[11] S. Matsumoto, Flows of the solid torus and fixed point free homeomorphisms of the plane, unpublished.

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

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