Sub-Euclidean space

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

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