$π$-spaces and their open images

Mikhail Patrakeev; Vlad Smolin

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arXiv · 2208.06288

$π$-spaces and their open images

Mikhail Patrakeev·Vlad Smolin

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Abstract

We study spaces that can be mapped onto the Baire space (i.e. the countable power of the countable discrete space) by a continuous quasi-open bijection. We give a characterization of such spaces in terms of Souslin schemes and call these spaces $π$-spaces. We show that every space that has a Lusin $π$-base is a $π$-space and that every second-countable $π$-space has a Lusin $π$-base. The main result of this paper is a characterization of continuous open images of $π$-space.

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BibTeX RIS

Mikhail Patrakeev, Vlad Smolin. 2022-08-12. $π$-spaces and their open images. https://arxiv.org/abs/2208.06288

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