Meaning of locally Euclidean space

lo'cally Euclid'ean space'

Pronunciation: [key]
— Math. Math.
  1. a topological space in which each point has a neighborhood that is homeomorphic to an open set in a Euclidean space of specified dimension.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.