Open Sets in Metric Space

Theorem

Let $M = \struct {A, d}$ be a metric space.


Then $\O$ and $A$ are both open in $M$.


Proof

We have the results:

Empty Set is Open in Metric Space
Metric Space is Open in Itself

$\blacksquare$


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: Example $2.3.10$
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