Metrizable space

This article defines a property of topological space that is pivotal (viz important) among currently studied properties of topological spaces

This article is about a basic definition in topology.
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Definition

Symbol-free definition

A topological space is said to be metrizable if it occurs as the underlying topological space of a metric space.

Relation with other properties

Stronger properties

• Completely metrizable space

Weaker properties

• Perfectly normal space
• Paracompact Hausdorff space
• Paracompact space