Can any one tell me in simple words what is a compact set? I read the definition of Compact set, but do not get it. BTW, I do not know topology.
In particular, is the probability simplex, $W\ge0, W1=1$, a compact set?
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One useful characterization, especially as regards optimization: a set $S$ (in a metric space) is compact if and only if every continuous function on $S$ has a maximum.