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

See also

• Quotient topology
• Passing to the quotient

References

1. Jump up ↑ Introduction to topological manifolds - John M Lee - Second edition