J. Schr\"oder
Natural sinks on $Y_\beta $

Comment.Math.Univ.Carolinae 33,1 (1992) 173-180.

Abstract:Let ${(e_\beta : {\bold Q} \rightarrow Y_\beta )}_{\beta \in \text {Ord}}$ be the large source of epimorphisms in the category ${\text {Ury}}$ of Urysohn spaces constructed in [2]. A sink ${(g_\beta : Y_\beta \rightarrow X)}_{\beta \in \text {Ord}}$ is called natural, if $g_\beta \circ e_\beta = g_{\beta '} \circ e_{\beta '}$ for all $\beta ,\beta ' \in \text {Ord}$. In this paper natural sinks are characterized. As a result it is shown that $\text {Ury}$ permits no $({Epi},{\Cal M})$-factorization structure for arbitrary (large) sources.

Keywords: epimorphism, Urysohn space, cointersection, factorization, natural sink, periodic, cowellpowered, ordinal
AMS Subject Classification: 18A20, 18A30, 18B30, 54B30, 54C10, 54D10, 54D35, 54G20

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