Topology

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.

In mathematics, a ringed space can be equivalently thought of either (a) a space together with a collection of commutative rings, the elements of which are "functions" on each open set of the space.

Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

The Penrose triangle, also known as the Penrose tribar, or the impossible tribar, is an impossible object.

A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.

In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis.

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball, (viz., analogous to a circular object in two dimensions).

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.

In mathematics, a metric space is a set for which distances between all members of the set are defined.

The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology.

In algebra, a linear topology on a left A-module M is a topology on M that is invariant under translations and admits a fundamental system of neighborhood of 0 that consists of submodules of M.

In mathematics, a pointed space is a topological space with a distinguished point, the basepoint.

In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.

In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

In topology, a branch of mathematics, the clutching construction is a way of constructing fiber bundles, particularly vector bundles on spheres.

In mathematics, a covering number is the number of spherical balls of a given size needed to completely cover a given space, with possible overlaps.