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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Topologia i T. Mnogości


Preservation of some covering type properties by linear homeomorphisms of function spaces: Part 2

Prelegent: Mikołaj Krupski

2022-06-01 16:15

In the second part of my talk I will show some proof techniques. The talk should  be accessible regardless of listening to part 1.

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.