26 relations: Algebraic topology, Annulus (mathematics), Area, Area of a circle, Ball (mathematics), Bijection, Brouwer fixed-point theorem, Cartesian coordinate system, Circle, Circular symmetry, Compact space, Continuous function, Contractible space, Disk algebra, Euler characteristic, Fixed point (mathematics), Fundamental group, Geometry, Homeomorphism, Homology (mathematics), Homotopy, Orthocentroidal circle, Plane (geometry), Spelling of disc, Surjective function, Unit disk.
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
In mathematics, an annulus (the Latin word for "little ring" is anulus/annulus, with plural anuli/annuli) is a ring-shaped object, a region bounded by two concentric circles.
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
In geometry, the area enclosed by a circle of radius is.
In mathematics, a ball is the space bounded by a sphere.
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
A circle is a simple closed shape.
In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
In functional and complex analysis, the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions where D is the open unit disk in the complex plane C, f extends to a continuous function on the closure of D. That is, where H^\infty(\mathbf) denotes the Banach space of bounded analytic functions on the unit disc D (i.e. a Hardy space).
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and its centroid at opposite ends of a diameter.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
Disc and disk are two variants of the English word for objects of a generally thin and cylindrical geometry.
In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x).
In mathematics, the open unit disk (or disc) around P (where P is a given point in the plane), is the set of points whose distance from P is less than 1: The closed unit disk around P is the set of points whose distance from P is less than or equal to one: Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself.