Example:Continuous maps contracting something to a point

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Example

$(X,\mathcal{ J })$ $(Y,\mathcal{ K })$
The spaces in play

Let $(X,\mathcal{ J })$ and $(Y,\mathcal{ K })$ be topological spaces which are subspaces of $\mathbb{R}^2$ as shown on the right. Then we claim:

• there is a continuous mapping, $f:X\rightarrow Y$, that is also surjective.