Subspaces of pseudoradial spaces

Martin Sleziak

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arXiv · 1108.3536

Subspaces of pseudoradial spaces

Martin Sleziak

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Abstract

We prove that every topological space (T0-space, T1-space) can be embedded in a pseudoradial space (in a pseudoradial T0-space, T1space). This answers the Problem 3 in [Arhangelskii, A.V. - Isler, R. - Tironi, G: On pseudo-radial spaces, Comment. Math. Univ. Carolin. 27 (1986), 137-156]. We describe the smallest coreflective subcategory A of Top such that the hereditary coreflective hull of A is the whole category Top. (The same result without any separation axiom was proved already in the master thesis E. Murtinov\'a: Podprostory pseudoradi\'aln\'ich prostor\r{u}. I wasn't aware of this work when preparing this paper.)

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Martin Sleziak. 2011-08-17. Subspaces of pseudoradial spaces. https://arxiv.org/abs/1108.3536

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