Counting Banach spaces C(K)

Speaker(s)

Witold Marciszewski

Affiliation

University of Warsaw

Language of the talk

English

Date

Feb. 26, 2025, 4:15 p.m.

Room

room 5050

Seminar

Topology and Set Theory Seminar

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The talk will be devoted to presenting the results of a joint research project with Maciej Korpalski (UWr).
We studied the problem of isomorphic classification of the Banach spaces C(K) of real continuous functions on K, where K is a compact, separable, linearly ordered space of weight alef_1.
More precisely, we were interested in the question: how many isomorphic types of such spaces C(K) are there?

We showed that the answer to this question depends on additional set-theoretic axioms. In particular, assuming the continuum hypothesis, there are 2^c (c - continuum) such types, and assuming a certain axiom proposed by Baumgartner, there is only one type.

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