Topology

Major advances in the beginning of 20th century was the formalization of abstract algebra and topology; these two fields were deeply influenced by the pure mathematics philosophy.

Topology, branch of mathematics, sometimes referred to as rubber sheet geometry, in which two objects are considered equivalent if they can be continuously deformed into one another.

the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations

It states that for any continuous function f mapping a nonempty compact convex set to itself, there is a point x0 such that f(x0) = x0.

a metric space is a set together with a notion of distance between its points

a manifold is a topological space that locally resembles Euclidean space near each point

His contributions include the Atiyah-Singer index theorem and co-founding topological K-theory.

In the mathematical field of geometric topology, the Poincare conjecture is a theorem about the characterization of the 3-sphere.

In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poinca

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

provides an instructive example of some ideas in topology.

In topology, the degree or Brouwer degree of a continuous mapping between two compact oriented manifolds of the same dimension is

In topology, a branch of mathematics, the smash product of two pointed spaces (i.e.

is one of the most important unsolved problems in topology.

In topology in mathematics, Freedman's classification (or Freedman's theorem) is a central result about four-dimensional topologic

heorem (after Nicolaas Kuiper) is a result on the topology of operators on an infinite-dimensional, complex Hilbert space H.

point in its unitary dual equipped with the Fell topology.

general topology

topological spaces

fundamental results in topology

topology

specializing in topology