Frequently Asked Questions...
In a compact space X with metric d. True that for d(x,y)>=e iff B(x,e/2) and B(y,e/2) don't intersect?
B(x,e/2) is the open ball of radius e/2 centered at x.
Answer:
False actually. It is true that d(x, y)≥e implies that B(x, e/2)∩B(y, e/2) = ∅, however there are compact metric spaces where B(x, e/2)∩B(y, e/2) = ∅ yet d(x, y) Topology #4 Open Balls Here are a list of other products on Woodturning Tools, come check these out:
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