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## Homework Statement

Let K be a compact subset of a metric space M, and let {U_α}_α∈I be an open cover of

K. Show that there is a positive real number δ with the property that for every x ∈ K there is

some α ∈ A with B_δ (x) ⊆ U_α.

## Homework Equations

n/a

## The Attempt at a Solution

Since U_α are open, every point of them is a an interior point. For any positive δ, B_δ (x) [itex]\subset[/itex] U_α, for some α?

I'm lost here, anything I think seems trivial...