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Continua and their non-separating subcontinua

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Bennett D. E., Fugate J. B.

Instytut Matematyczny Polskiej Akademii Nauk

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

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1 Bennett D. E.

1 Fugate J. B.

1 1977

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Continua and their non-separating subcontinua