Flashcards: Topology

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 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.

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

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

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

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 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.

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

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

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.

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.