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.

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The same result without any separation axiom was proved already in the master thesis E. Murtinová: Podprostory pseudoradiálních prostorů. I wasn't aware of this work when preparing this paper.