A tale of three hedgehogs

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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 Fσ sets.