Natural sinks on $Y_{\beta }$

Schröder, J.. "Natural sinks on $Y_\beta $." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 173-179. <http://eudml.org/doc/247377>.

@article{Schröder1992,
abstract = {Let $\{(e_\beta : \{\mathbf \{Q\}\} \rightarrow Y_\beta )\}_\{\beta \in \text\{\bf Ord\}\}$ be the large source of epimorphisms in the category $\text\{\bf Ury\}$ of Urysohn spaces constructed in [2]. A sink $\{(g_\beta : Y_\beta \rightarrow X)\}_\{\beta \in \text\{\bf Ord\}\}$ is called natural, if $g_\beta \circ e_\beta = g_\{\beta ^\{\prime \}\} \circ e_\{\beta ^\{\prime \}\}$ for all $\beta ,\beta ^\{\prime \} \in \text\{\bf Ord\}$. In this paper natural sinks are characterized. As a result it is shown that $\text\{\bf Ury\}$ permits no $(\{Epi\},\{\mathcal \{M\}\})$-factorization structure for arbitrary (large) sources.},
author = {Schröder, J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {epimorphism; Urysohn space; cointersection; factorization; natural sink; periodic; cowellpowered; ordinal; factorization structure; Urysohn space; epimorphism; cowellpowered; sink; source},
language = {eng},
number = {1},
pages = {173-179},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Natural sinks on $Y_\beta $},
url = {http://eudml.org/doc/247377},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Schröder, J.
TI - Natural sinks on $Y_\beta $
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 173
EP - 179
AB - Let ${(e_\beta : {\mathbf {Q}} \rightarrow Y_\beta )}_{\beta \in \text{\bf Ord}}$ be the large source of epimorphisms in the category $\text{\bf Ury}$ of Urysohn spaces constructed in [2]. A sink ${(g_\beta : Y_\beta \rightarrow X)}_{\beta \in \text{\bf Ord}}$ is called natural, if $g_\beta \circ e_\beta = g_{\beta ^{\prime }} \circ e_{\beta ^{\prime }}$ for all $\beta ,\beta ^{\prime } \in \text{\bf Ord}$. In this paper natural sinks are characterized. As a result it is shown that $\text{\bf Ury}$ permits no $({Epi},{\mathcal {M}})$-factorization structure for arbitrary (large) sources.
LA - eng
KW - epimorphism; Urysohn space; cointersection; factorization; natural sink; periodic; cowellpowered; ordinal; factorization structure; Urysohn space; epimorphism; cowellpowered; sink; source
UR - http://eudml.org/doc/247377
ER -