Euclidean space(noun)

a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional

Euclidean space(Noun)

Ordinary two- or three-dimensional space, characterised by an infinite extent along each dimension and a constant distance between any pair of parallel lines.

Euclidean space(Noun)

Any real vector space on which a real-valued inner product (and, consequently, a metric) is defined.