module appears to be a linear space; is it algebraic or geometric? In particular, when it is finite-dimensional, over real numbers, and endowed with inner product, it becomes Euclidean space; now geometric. The (algebraic?) field of real numbers is the same as the (geometric?) real line. Its algebraic closure, the (algebraic?) field of complex numbers, is the same as the (geometric?) complex plane. It is first of all "a place we do analysis" (rather than algebra or geometry). Every space treated in Section "Types of spaces" above, except for "Non-commutative geometry", "Schemes" and "Topoi" subsections, is a set (the "principal base set" of the structure, according to Bourbaki) endowed with some additional structure; elements of the base set are usually called "points" of this space. In contrast, elements of (the base set of) an algebraic structure usually are not called "points". However, sometimes one uses more than one principal base set. For example, two-dimensional projective geometry may be formalized via two base sets, the set of points and the set of lines. Moreover, a striking feature of projective planes is the symmetry of the roles played by points and lines. A less geometric example: a graph may be formalized via two base sets, the set of vertices (called also nodes or points) and the set of edges (called also arcs or lines). Generally, finitely many principal base sets and finitely many auxiliary base sets are stipulated by Bourbaki. Many mathematical structures of geometric flavor treated in the "Non-commutative geometry", "Schemes" and "Topoi" subsections above do not stipulate a base set of points. For example, "pointless topology" (in other words, point-free topology, or locale theory) starts with a single base set whose elements imitate open sets in a topological space (but are not sets of points); see also mereotopology and point-free geometry. Mathematical spaces by name Affine space Algebraic space Baire space Banach space Base space Bergman space Berkovich space Besov space Borel space Calabi-Yau space Cantor space Cauchy space Cellular space Chu space Closure space Conformal space Complex analytic space Dimension Drinfeld's symmetric space Eilenberg–Mac Lane space Euclidean space Fiber space Finsler space First-countable space Fréchet space Function space G-space Green space (topological space) Hardy space Hausdorff space Heisenberg space Hilbert space Homogeneous space Inner product space Kolmogorov space Lp-space Lens space Liouville space Locally finite space Loop space Lorentz space Mapping space Measure space Metric space Minkowski space Müntz