Difference between revisions of "Universal property of the quotient topology"
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Revision as of 07:26, 27 April 2015
Statement
\require{AMScd} \begin{CD} (X,\mathcal{J}) @>p>> (Y,\mathcal{Q}_p)\\ @VVV @VVfV\\ \searrow @>>f\circ p> (Z,\mathcal{K}) \end{CD}
The characteristic property of the quotient topology states that[1]:
f is continuous if and only if f\circ p is continuous
[Expand]
Proof that the quotient topology is the unique topology with this property
See also
References
- Jump up ↑ Introduction to topological manifolds - John M Lee - Second edition
