Open Ball of Point Inside Open Ball/Metric Space/Illustration

Illustration of Open Ball of Point Inside Open Ball: Metric Space

This diagram illustrates the proof of Open Ball of Point Inside Open Ball: Metric Space in $M = \struct {\R^2, d_2}$:

In $\R^2$, we can draw a circle of radius $\delta$ whose center is $y$ lying entirely within the larger circle of radius $\epsilon$ whose center is $x$ .

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.3$: Open sets in metric spaces: Lemma $2.3.7$