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Continua and their non-separating subcontinua

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Rozprawy Matematyczne tom/nr w serii: 149 wydano: 1977
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CONTENTS

Introduction......................................................................................................................................... 5

Preliminaries...................................................................................................................................... 6

Chapter I. Basic types and properties of non-separating continua......................................... 7
 Terminal and end continua......................................................................................................... 7
 Terminal continua and irreduisibility......................................................................................... 9
 Composants and E-continua..................................................................................................... 13

Chapter II. Necessary and sufficient conditions for irreducibility.............................................. 18
 Decompositions into terminal continua................................................................................... 18
 Triods and Sorgenfrey's Theorems.......................................................................................... 20

Chapter III. Terminal and non-cutting continua............................................................................ 20
 Properties of terminal and non-cutting continua..................................................................... 26
 Local connectivity at K and K-aposyndesis.............................................................................. 27
 Arc and monotone decompositions.......................................................................................... 31
Chapter IV. Absolutely non-separating continua.................................................................................. 34
 Basic types and properties......................................................................................................... 34
 Hereditarily irreducible continua................................................................................................ 38

Chapter V. Minimal continua............................................................................................................ 41
 Existence of certain minimal continua...................................................................................... 41
 The structure of minimal continua............................................................................................. 43
References.................................................................................................................................................. 45
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 149
Liczba stron
46
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXLIX
Daty
wydano
1977
Twórcy
Bibliografia
  • [1] D. E. Bennett, A sufficient condition for countable-set aposyndesis, Proc. Amer. Math. Soc. 32 (1972), pp. 578-584.
  • [2] R. H. Bing, Snake-like continua, Duke Math. J. 18(1951), pp. 653-663.
  • [3] J. L. Cornette, Problem No P 487, R1, Colloq. Mathematicum 17 (1967), p. 366.
  • [4] J. B. Fugate, Decomposable chainable continua. Trans. Amer. Math. Soc. 123 (1966), pp. 460-468.
  • [5] J. B. Fugate, A characterisation of chainable continua, Canadian J. Math. 21 (1969), pp. 383-393.
  • [6] G. R. Gordh, Jr., Terminal subcontinua of hereditarily unicoherent continua, Pacific. J. Math. 47 (1973), pp. 457-464.
  • [7] J. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass. 1961.
  • [8] F. B. Jones, Aposyndetic continua and certain boundary conditions, Amer. J. Math. 63 (1941), pp. 545-553.
  • [9] K. Kuratowski, Topologie, Vol. II, PWN — Academic Press, Warszawa-New York 1968.
  • [10] H. C. Miller, On unicoherent continua, Trans. Amer. Math. Soc. 69 (1950), pp. 179-194.
  • [11] R. H. Rosen, On three-like continua and irreducibility, Duke Math. J. 26 (1959), pp. 113-122.
  • [12] R. H. Sorgenfrey, Concerning triodic continua, Amer. J. Math. 66 (1944), pp. 439-460.
  • [13] R. H. Sorgenfrey, Concerning continua irreducible about n points, Amer. J. Math. 68 (1946), pp. 667-671.
  • [14] E. S. Thomas Jr., Monotone decompositions of irreducible continua, Rozprawy Matematyczne (Dissertationes Mathematicae) 50 (1966).
  • [16] G. T. Whyburn, Analytical Topology, Amer. Math. Soc. Colloq. Pub. 28, Providence, R. I. 1942.
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