A greedy, partially optimal proof of the Heine-Borel Theorem
نویسنده
چکیده
The Heine-Borel theorem states that any open cover of the closed interval Œa; b contains a nite subcover. We give a new, constructive proof inspired by the concept of a greedy algorithm. In the case when the initial cover consists only of intervals, our proof is optimal in that it constructs a nite subcover with the fewest possible number of elements. Our work leaves open a number of questions which are discussed in the nal section.
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تاریخ انتشار 2017