Let metric space $X$ and fixed point $a\in X$ be given. I search for not restrictive assumption under what all balls in metric space $X$ with center in $a$ have the cardinality equal the carinality of $X$.
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2Define not restrictive. – Asaf Karagila Feb 03 '14 at 19:45
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I know for example that this property have balls in normed spaces. It is too much restrictive. – Alex Feb 03 '14 at 19:53