III.93 Universal Covers and and III.94 Variational Methods by Lawrence C. Evans: Pages 309 – 310.

Universal Covers.

A cover of a space X is a space Y and a continuous surjection from Y to X such that the inverse image of a small neighborhood in X is a disjoint union of small neighborhoods in Y.

How is a cover related to a random variable, where inverse images of open sets are open?

If U is a universal cover of X and and Y is any other cover of X, then U can be made into a cover of Y in a natural way.

Variational Methods by Lawrence C. Evans.

Critical points.

One-dimensional variational problems.

Shortest distance in a plane is a straight line.

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