Preservation of some covering type properties by linear homeomorphisms of function spaces

Prelegent(ci)

Mikołaj Krupski

Afiliacja

University of Warsaw

Termin

25 maja 2022 16:15

Pokój

p. 4420

Seminarium

Seminarium „Topologia i teoria mnogości”

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An old question of Arhangel'skii asks if (a) the Lindelof property (b) the Menger property of a Tychonoff space X is preserved by homeomorphisms of the space C_p(X) of continuous functions on X equipped with the pointwise topology. A celebrated Velichko's theorem [Topol. Appl. 89, (1998)] provides the affirmative answer to part (a) of this question for linear homeomorphisms of C_p(X)-spaces. In this talk I will show that a similar result (for linear homeomorphisms) holds for part (b). The proof is based on a new method that can also be applied to prove analogous theorems for other, related covering type properties.

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