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Let f be a continuous from a topological space X to the reals. Let a be...

Let f be a continuous from a topological space X to the reals. Let a be in the reals and let A = {x in X : f(x)=a} Show that A is closed inX.

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Topology is the study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid.

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