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Natural sinks on Y β

J. Schröder (1992)

Commentationes Mathematicae Universitatis Carolinae

Let ( e β : 𝐐 Y β ) β Ord be the large source of epimorphisms in the category Ury of Urysohn spaces constructed in [2]. A sink ( g β : Y β X ) β Ord is called natural, if g β e β = g β ' e β ' for all β , β ' Ord . In this paper natural sinks are characterized. As a result it is shown that Ury permits no ( E p i , ) -factorization structure for arbitrary (large) sources.

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