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On absolute retracts of ω*

100%

Bella A., Błaszczyk A., Szymański A.

Fundamenta Mathematicae

1994

tom 145

nr 1

1-13

An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight $ω_1$ is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same π-weight), then X is homeomorphic to the Gleason space over the Cantor cube ${0,1}^{ω_1}$.

Embeddings into 𝓟(ℕ)/fin and extension of automorphisms

76%

Bella A., Dow A., Hart K., Hrusak M., van Mill J., Ursino P.

Fundamenta Mathematicae

2002

tom 174

nr 3

271-284

Given a Boolean algebra 𝔹 and an embedding e:𝔹 → 𝓟(ℕ)/fin we consider the possibility of extending each or some automorphism of 𝔹 to the whole 𝓟(ℕ)/fin. Among other things, we show, assuming CH, that for a wide class of Boolean algebras there are embeddings for which no non-trivial automorphism can be extended.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Bella A.

1 Błaszczyk A.

1 Dow A.

1 Hart K.

1 Hrusak M.

1 Szymański A.

1 Ursino P.

1 van Mill J.

1 2002

1 1994

Wyniki wyszukiwania

On absolute retracts of ω*

Embeddings into 𝓟(ℕ)/fin and extension of automorphisms