$\pi$-spaces and their open images
Mikhail Patrakeev, Vlad Smolin

TL;DR
This paper introduces $ ext{-spaces},$ characterizes them via Souslin schemes, and explores their open images, establishing connections with Lusin $ ext{-bases}$ and second-countability.
Contribution
It defines $ ext{-spaces},$ characterizes their properties, and provides a main result describing their continuous open images in terms of topological bases.
Findings
Every space with a Lusin $ ext{-base}$ is a $ ext{-space}$.
Every second-countable $ ext{-space}$ has a Lusin $ ext{-base}.
Main result characterizes continuous open images of $ ext{-spaces}$.
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 -spaces. We show that every space that has a Lusin -base is a -space and that every second-countable -space has a Lusin -base. The main result of this paper is a characterization of continuous open images of -space.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras
