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The Menger curve Characterization and extension of homeomorphisms of non-locally-separating closed subsets

Seria
Rozprawy Matematyczne tom/nr w serii: 252 wydano: 1986
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Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction.................................................................................................................................................5
2. Partitioning Peano continua......................................................................................................................10
3. Peano continua and cross-connectedness...............................................................................................18
4. The characterization of the Menger curve.................................................................................................28
5. Extension of homeomorphisms on non-locally-separating, closed subsets of the Menger curve..............34
6. Universality and map extension theorems.................................................................................................42
7. Bibliography..............................................................................................................................................45
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 252
Liczba stron
45
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLII
Daty
wydano
1986
Twórcy
autor
  • University of Alabama in Birmingham, Birmingham, Alabama 35294, U.S.A.
  • University of Alabama in Birmingham, Birmingham, Alabama 35294, U.S.A
  • University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO
Bibliografia
  • [A,1] R. D. Anderson, A characterization of the Universal Curve and a proof of its homogeneity, Ann. of Math. 67 (1958), 313-324.
  • [A,2] R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. 68 (1958), 1-16.
  • [B,1] R. H. Bing, Complementary domains of continuous curves, Fund. Math. 36 (1949), 306-318.
  • [B,2] R. H. Bing, Partitioning continuous curves, BAMS 58 (1952), 536-556.
  • [Bo] H. G. Bothe, Universalmengen bezüglich der Lage im $E^n$, Fund. Math 56 (1964), 203-212.
  • [B-M] L. M. Blumenthal and K. Menger, Studies in Geometry, Freeman, San Francisco, CA, 1976.
  • [Ca] J. W. Cannon, A positional characterization of the (n-1)-dimensional Sierpiński curve in $S^n$ (n≠4). Fund. Math. 79 (1973), 107-112.
  • [C] S. Claytor. Topological immersion of Peanian continua in a spherical surface, Ann. of Math. 35 (1934). 809-835.
  • [H] S.-T. Hu, Homology Theory: A First Course in Algebraic Topology, Holden-Day, San Francisco, CA, 1966.
  • [H-W] W. Hurewicz and H. Wallman, Dimension Theory, Princeton University Press, Princeton, NJ, 1948.
  • [K,1] C. Kuratowski, Sur les problème des courbes gauches en Topologie, Fund. Math. 15 (1930), 271-283.
  • [K,2] C. Kuratowski, Topology II, Academic Press. New York 1968.
  • [L] S. Lefschetz, On compact spaces, Ann. of Math. 32 (1931), 521-538.
  • [M] K. Menger, Kurventheorie, Teubner. Berlin/Leipzig 1932.
  • [P] B. A. Pasynkov, Partial Topological Products, Trans. Moscow Math. Soc. for 1965, 153-271 (Trudy Mos. Mal. Obsc. 13 (1965), 136-245.)
  • [Wa,1] J. J. Walsh, Monotone and open mappings on manifolds, I, TAMS 209 (1975), 419-432.
  • [Wa,2] J. J. Walsh, Light open and open mappings on manifolds, II, TAMS 217 (1976), 271-284.
  • [W] G. T. Whyburn, Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, AMS, Providence. RI, 1942.
  • [Wi,1] D. C. Wilson, Open mappings of the Menger curve onto continuous curves, TAMS 168 (1972), 497-515.
  • [Wi,2] D. C. Wilson, Open mappings on manifolds and counterexample to the Whyburn conjecture, Duke Math. J. 40 (1973), 705-716.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-1d60f6d5-8102-4734-9186-d4b4bfd8f2dc
Identyfikatory
ISBN
83-01-06691-1
ISSN
0012-3862
Kolekcja
DML-PL
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