Open ball
Let $(X, \rho)$ - a metric-space
Set $O_{\varepsilon}(x) = {y \in X: \rho(x, y) < \varepsilon}$ considered an open ball.
Properties
- Open ball is an open-set in topology incuced by the metric (see in metric-space).
Let $(X, \rho)$ - a metric-space
Set $O_{\varepsilon}(x) = {y \in X: \rho(x, y) < \varepsilon}$ considered an open ball.