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Jun5-07, 06:18 PM
Sci Advisor
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mathwonk's Avatar
P: 9,499
consider a statement of form "for all elements of set S, property P is true".

If S is empty this statement is true, :"vacuously".

this aNSWERS YOUR QUESTION, say in a metric space. i.e. openness is defined by a ":universal" quntifier: "for all p in S, there is an open ball around p also contained in S".