<p>What are the open and closed balls in the metric space of [example 4, sec 1]?

Question

<p>What are the open and closed balls in the metric space of [example 4, sec 1]? Show that 2 balls of different centers and radii may be equal. What are the open sets in this metric space?</p>
<p>&#160;</p>
<p>Example 4 section 1:</p>
<p>Let E be an arbitrary set and, for&#160;<img src="https://s3.amazonaws.com/answer-board-image/cramster-equation-2012221233206346378280018531636852.gif" alt="" align="absmiddle" />, define d(p,q)=0 if p=q, d(p,q)=1 if p&#8800;q.</p>

Explanation / Answer

A metric space is a set E with a distance function d(x,y) :ExE -->R+ into the positive real numbers that mimics the absolute value function. So d satisfies i) d(x,y)>=0 and ii) d(x,z)

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