Example:Continuous maps contracting something to a point
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Example

The spaces in play 

Let [ilmath](X,\mathcal{ J })[/ilmath] and [ilmath](Y,\mathcal{ K })[/ilmath] be topological spaces which are subspaces of [ilmath]\mathbb{R}^2[/ilmath] as shown on the right. Then we claim:
 there is a continuous mapping, [ilmath]f:X\rightarrow Y[/ilmath], that is also surjective.