Characterizations of Urysohn-closed spaces
On absolute retracts of ω*
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 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...
Embeddings into 𝓟(ℕ)/fin and extension of automorphisms
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.
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