Noun
a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
Source: WordNetThe victory over Euclidean space was not achieved by isolated individuals, but by a field of young rebels opposed to all absolutes. Marshall McLuhan
The Greeks encountered the confusion of tongues when numbers invaded Euclidean space. Marshall McLuhan
Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience. Arthur Cayley
A characterization of finite dimensionality is that a Hausdorff TVS is locally compact if and only if it is finite-dimensional (therefore isomorphic to some Euclidean space). Source: Internet
A Klein bottle can be produced by gluing two Möbius strips together along their edges; this cannot be done in ordinary three-dimensional Euclidean space without creating self-intersections. Source: Internet
A continuous map from a closed ball of Euclidean space to its boundary cannot be the identity on the boundary. Source: Internet