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- W2011476742 abstract "This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff k- spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure." @default.
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- W2011476742 date "1996-08-01" @default.
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- W2011476742 title "Reflexive objects in topological categories" @default.
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- W2011476742 doi "https://doi.org/10.1017/s0960129500001079" @default.
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