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A decomposition of $E^3$ into straight arcs and singletons

Seria
Rozprawy Matematyczne tom/nr w serii: 73 wydano: 1970
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Abstrakty
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CONTENTS
1. Introduction............................................................................................................................................. 5
2. Notation and. terminology................................................................................................................... 6
3. Description of G.................................................................................................................................... 6
4. Preliminaries to the main result........................................................................................................ 13
5. The main result..................................................................................................................................... 15
6. Lemmas on Property X......................................................................................................................... 16
7. Construction of certain open sets...................................................................................................... 20
8. Constructing homotopy centerlines.................................................................................................. 24
9. Patterns on the sides of Δ.................................................................................................................. 28
10. The AB-condition................................................................................................................................. 30
11. Types of simple closed curves......................................................................................................... 32
12. Similar patterns................................................................................................................................... 36
13. Property II.............................................................................................................................................. 40
14. Construction of homotopy-$h[Γ_α]'s$............................................................................................. 42
15. Proof of Lemma 3................................................................................................................................ 45
References.................................................................................................................................................. 46
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 73
Liczba stron
46
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXXIII
Daty
wydano
1970
Twórcy
  • The University of Iowa, Iowa City, Iowa
Bibliografia
  • [1] S. Armentrout, Decompositions of $E^3$ with a compact O-dimensional set of nondegenerate elements, Trans. Amer. Math. Soc. 123 (1966), pp. 165-177.
  • [2] S. Armentrout, A three-dimensional spheroidal space which is not a sphere (to appear).
  • [3] R. H. Bing, What topology is here to stayl, Summary of Lectures and. Seminars, Summer Institute on Set Theoretic Topology, University of Wisconsin, 1955 (revised (1958)), pp. 25-27.
  • [4] R. H. Bing, Upper semicontinuous decompositions of $E^3$, Ann. of Math. 65 (1957), pp. 363-374.
  • [5] R. H. Bing, A decomposition of $E^3$ into points and tame arcs such that the decomposition space is topologically different from $E^3$, Ann. of Math. 65 (1957), pp. 484-500.
  • [6] R. H. Bing, Point-like decompositions of $E^3$, Fund. Math. 50 (1962), pp. 431-453.
  • [7] A. J. Boals, Two separation theorems for compact sets (to appear).
  • [8] L. O. Cannon, On a point-segment decomposition of $E^3$ defined by McAuley, Notices Amer. Math. Soc. 14 (1967), p. 91.
  • [9] L. F. McAuley, Some upper semicontinuous decompositions of $E^3$ into $E^3$, Ann. of Math. 73 (1961), pp. 437-457.
  • [10] L. F. McAuley, Another decomposition of $E^3$ into points and intervals, Topology Seminar Wisconsin, 1965, Princeton University Press, 1966, pp. 33—51.
  • [11] R. L. Moore, Foundations of Point Set Theory, Amer. Math. Soc. Colloquium Publications, vol 13 (rev. ed.), Providence 1962.
  • [12] R. B. Sher, Toroidal decompositions of $E^3$, Fund. Math. 61 (1968), pp. 225-241.
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