What is it about?

We investigate possible images of Bernstein subsets of polish spaces. For example, a whole real line can be such an image but no proper co-analytic set can be a continuous image of a Bernstein set.

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Why is it important?

In our research, a new class of topological spaces plays an important role: these are X spaces for which there there exists a continuous mapping from X onto X such that the inverse image of every point in X has size continuum (we call this spaces fiberable).

Perspectives

The initial idea of the research was the following observation: the Cantor space X is isomorphic with its product X x X.

Jacek Cichoń
Politechnika Wroclawska

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This page is a summary of: Images of Bernstein sets via continuous functions, Georgian Mathematical Journal, December 2019, De Gruyter, DOI: 10.1515/gmj-2019-2041.
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