The complement of a $\sigma$-compact subset of a space with a $\pi$-tree also has a $\pi$-tree

Mikhail Patrakeev

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arXiv · 1512.02458

The complement of a $\sigma$-compact subset of a space with a $\pi$-tree also has a $\pi$-tree

Mikhail Patrakeev

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Abstract

We prove that the complement of a $\sigma$-compact subset of a topological space that has a $\pi$-tree also has a $\pi$-tree. To do this, we construct the foliage hybrid operation, which deals with foliage trees (that is, set-theoretic trees with a `leaf' at each node). Then using this operation we modify a $\pi$-tree of a space and get a $\pi$-tree for its subspace.

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BibTeX RIS

Mikhail Patrakeev. 2015-12-08. The complement of a $\sigma$-compact subset of a space with a $\pi$-tree also has a $\pi$-tree. https://arxiv.org/abs/1512.02458

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