Definition:Open Set (Metric Space)/Also known as

Open Set (Metric Space): Also known as

An open set in a metric space $M = \struct {A, d}$ can also be referred to as:

• an open set of $M$
• open in $M$
• a $d$-open set
• $d$-open.

An open set in $M$ is sometimes seen written as open subset of $A$.

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 $2.3.12$