Roman Pol's example of a Hurewicz set with one-dimensional square

Speaker(s)

Witold Marciszewski

Affiliation

University of Warsaw

Language of the talk

English

Date

May 6, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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Paul Erdos gave an example of a closed one-dimensional subspace X of a Hilbert space whose square X x X is also one-dimensional. On the other hand, it is known that such example cannot be sigma- compact.
However, Roman Pol recently proved that, consistently, we can find a Hurewicz (a property slightly weaker than sigma-compactness) subset X of the Euclidean plane with one-dimensional square X x X.

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