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 Poincaré conjecture (UK: , US: , French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere (the hypersphere that bounds the 4-ball in four-dimensional space).

the Hilbert-Smith conjecture is concerned with the possible transformation groups of manifolds

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

He was part of an influential school of topology at Princeton University

as well as topology

now remembered mostly for his 1871 paper on topology

who is considered to be one of the founders of modern topology

Stephen Smale (born July 15, 1930) is an American mathematician, known for his research in topology, dynamical systems and mathematical economics.

He is remembered as a pioneer of topology, which also takes its name from his work.

He was the discoverer and eponym of Boy's surface-a three-dimensional projection of the real projective plane without singularities, the first of its kind.

Isaac Namioka (April 25, 1928, September 25, 2019) was a Japanese-American mathematician who worked in general topology and functional analysis.

Heinz Hopf (19 November 1894-3 June 1971) was a German mathematician who worked on the fields of dynamical systems, topology and geometry. == Early life and education == Hopf was born in Gräbschen, German Empire (now Grabiszyn, part of Wrocław, Poland), the son of Elizabeth (née Kirchner) and Wilh

Willi Ludwig August Rinow (February 28th, 1907 in Berlin, March 29th, 1979 in Greifswald) was a German mathematician who specialized in differential geometry and topology.

He is primarily known for his contributions to set theory, topology, measure theory and graph theory.

Max Wilhelm Dehn (November 13, 1878, June 27, 1952) was a German mathematician most famous for his work in geometry, topology and geometric group theory.

He also gave fundamental contributions to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, functional analysis, algorithmic information theory and computational complexity.

In mathematics, a condensation point p of a subset S of a topological space is any point p such that every neighborhood of p contains uncountably many points of S.

A lens space is an example of a topological space, considered in mathematics.

In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a topologically invariant way.

Topology General Topology

Topology Spaces

of the 2-sphere into 3-dimensional Euclidean space. The topological object was discovered by J. W. Alexander (1924).

of a 3-sphere is a 4-ball. It is called a 3-sphere because topologically, the surface itself is 3-dimensional, even

contractible 2-dimensional CW complex

He is known for the Arf invariant in topology

Gustave Choquet was a French mathematician who worked in functional analysis, potential theory, topology and measure theory.

Herbert Robbins was an American mathematician and statistician who worked in topology, measure theory, statistics,and other fields.

Herbert Seifert was a German mathematician who made important contributions to topology and knot theory.

Karol Borsuk was a Polish mathematician who made important contributions to topology.

Leopold Vietoris was a long-lived Austrian mathematician best known for his contributions to topology, especially the Mayer-Vietoris sequence. He was also interested in mathematical history.

Pavel Aleksandrov was a Russian mathematician who made important contributions to general topology.

Reinhold Baer 's mathematical work was wide ranging; topology, abelian groups and geometry. His most important work, however, was in group theory, on the extension problem for groups, finiteness conditions, soluble and nilpotent groups.

Von Dyck made important contributions to function theory, group theory ( where a fundamental result on group presentations is named after him ) topology and potential theory.

Poul Heegaard was a Danish mathematician who ( with Max Dehn ) was the first to classify compact surfaces.