Metric Spaces MT23, Balls
Flashcards
Define the open ball $B(a, \varepsilon)$.
\[B(a, \varepsilon) = \{x \in X : d(x, a) < \varepsilon\}\]
Define the closed ball $\bar B(a, \varepsilon)$.
\[\bar B(a, \varepsilon) = \{x \in X : d(x, a) \le \varepsilon\}\]
Suppose $X$ is a metric space and $Y \subseteq X$. How can you write $B _ Y(a, \varepsilon)$?
\[B _ Y(a, \varepsilon) = Y \cap B _ X(a, \varepsilon)\]