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

Prelegent(ci)

Kacper Kucharski

Afiliacja

Doctoral School of Exact and Natural Sciences UW

Język referatu

polski

Termin

22 października 2025 16:15

Pokój

p. 4050

Seminarium

Seminarium „Topologia i teoria mnogości”

---

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.

---