A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that

A set \(\bigcup\) is open in the meric topology induced by d if and only for each x\(\epsilon\bigcup\), there exist \(\epsilon> 0\) such that

—>> B_d( x,\(\epsilon)\subset\bigcup\)

\(B_d( x,\epsilon)\supset\bigcup\)

\(B_d( x,\epsilon) = \bigcup\)

\(B_d( x,\epsilon)\) > \bigcup\)