Preservation of scattered-like properties by isomorphisms of function spaces and free Abelian topological groups

Speaker(s)

Kacper Kucharski

Affiliation

Doctoral School of Exact and Natural Sciences UW

Language of the talk

Polish

Date

Oct. 22, 2025, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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During the talk we will show that if a space X either satisfies the property (κ) or is strongly σ–scattered, then a space Y has to satisfy the same property, provided there exists a continuous linear surjection of the space Cp(X) of real-valued continuous functions on X, equipped with the pointwise converegence topology, onto the space Cp(Y). We will also provide a proof of the fact that scatterdness is an A-invariant property in the realm of first-countable spaces, i.e. if the free Abelian topological groups A(X) and A(Y) are topologically isomorphic, for some first-countable spaces X and Y, then X is scattered if and only if Y is scattered. This gives a partial solution to an old problem of Archangielski.
This is a joint work with Mikołaj Krupski.

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