Sub-Euclidean space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

Definition

Symbol-free definition

A topological space is termed sub-Euclidean if it can be embedded as a subspace of some (finite-dimensional) Euclidean space.

Relation with other properties

Stronger properties

• Compact differentiable manifold
• Compact metrizable manifold
• finite-dimensional compact metrizable space

Weaker properties

• Metrizable space
• Second-countable space
• Perfectly normal space
• Normal space
• Hausdorff space