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arXiv · 1711.08656

A tale of three hedgehogs

Igor Arrieta Torres
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Abstract

In this work we study three topologies defined over the same set: the hedgehog. As the name suggests, the hedgehog can be described as a set of spines identified at a single point. Among others, we give a proof of the Kowalsky hedgehog theorem, which asserts that every metrizable space is embeddable into a countable cartesian power of the metric hedgehog. Besides, the concept of collectionwise normality will characterized by means of a Tietze type extension theorem. In particular we give a proof of the fact that collectionwise normality is hereditary with respect to $F_{\sigma}$ sets.

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Igor Arrieta Torres. 2017-11-23. A tale of three hedgehogs. https://arxiv.org/abs/1711.08656

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