On zero-dimensional subspaces of Eberlein compacta

Speaker(s)

Witold Marciszewski

Affiliation

University of Warsaw

Date

March 7, 2018, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. We will discuss the following problem: Does every nonmetrizable Eberlein compact space contain a closed zero-dimensional, nonmetrizable subspace? We will construct a consistent counterexample. We conjecture that the answer to this problem is independent of ZFC and we will present a partial result justifying this conjecture.

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