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Containing spaces for planar rational compacta

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Mayer J. C., Tymchatyn E. D.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction.............................................................................5 2. Ordered scattered spaces......................................................6 2.1. Topological type..................................................................6 2.2. Ordered spaces..................................................................6 2.3. Rim-type.............................................................................9 2.4. Disk partitions.....................................................................9 3. Partition theorems.................................................................12 3.1. Partition Pullback Theorem...............................................13 3.2. Defining sequences of partitions.......................................13 3.3. a-Circlelacing lemmas.......................................................14 3.4. Brick Pulverizing Lemma...................................................15 3.5. Construction of a containing space...................................20 4. Embedding Theorem.............................................................21 5. Universal spaces...................................................................24 5.1. Question...........................................................................25 5.2. The Sierpiński curve.........................................................25 5.3. A conjectured universal planar rational space...................26 5.4. A conjectured universal planar space of rim-type ≤ a........26 References................................................................................26

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Universal rational spaces

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Mayer J. C., Tymchatyn E. D.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction......................................................................5 2. Rim-type and decompositions..........................................8 3. Defining sequences and isomorphisms..........................18 4. Embedding theorem.......................................................26 5. Construction of universal and containing spaces...........32 6. References....................................................................39

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

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Mayer J. C., Oversteegen L. G., Tymchatyn E. D.

Instytut Matematyczny Polskiej Akademii Nauk

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

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Inaccessibility, essential maps, and shape theory

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Brechner B. L., Mayer J. C., Tymchatyn E. D.

Fundamenta Mathematicae

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1989

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tom 132

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nr 1

1-23

Ograniczanie wyników

1 Fundamenta Mathematicae

4 Mayer J. C.

4 Tymchatyn E. D.

1 Brechner B. L.

1 Oversteegen L. G.

1 1990

1 1989

1 1988

1 1986

Containing spaces for planar rational compacta

Universal rational spaces

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

Inaccessibility, essential maps, and shape theory