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## Homework Statement

Let S = {(a,b) : 0 < a < b < 1 } Union {R} be a base for a topology. Find subsets M_1 and M_2 which are compact in this topology but whose intersection is not compact.

## Homework Equations

## The Attempt at a Solution

I'm not even sure what it means for an element of S to be compact, so I haven't been able to make any attempt at a solution.