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並前往https://wiki.math.ntnu.no/_media/tma4225/2014h/compactness.pdf

A subset K ⊆ R is called compact if, whenever O is a set of ...

Pick some c ∈ C with c > s −ε (it exists by the definition of s). Then there is a finite subcover Q of O for [a,c]. But then Q∪{U} is a finite subcover of ...

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