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Pełne teksty:
Warianty tytułu
Abstrakty
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
autor
autor
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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