Constructions and applications of rigid spaces, I

Kannan, V. ; Rajagopalan, M. (1978) Constructions and applications of rigid spaces, I Advances in Mathematics, 29 (1). pp. 89-130. ISSN 0001-8708

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The two major results proved are: (1) The category TOP of topological spaces contains a complete nonreflective subcategory. (2) Under the assumption (2m)+ < 22m, for each infinite cardinal number m there exists a Hausdorff space of cardinality m, in which the identity map is the only nonconstant continuous self-map. The first result is proved as a consequence of another result which answers a question of Herrlich concerning strongly rigid spaces; it is then used to settle in the negative a conjecture concerning the characterization of reflective subcategories in TOP. In addition, several interesting spaces are constructed.

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