For the topology of pointwise convergence, see Algebraic topology (object).
A torus, one of the most frequently studied objects in algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.
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Algebraictopology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...
proofs. Algebraictopology is a branch of mathematics that uses tools from algebra to study topological spaces. The basic goal is to find algebraic invariants...
In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from...
This is a list of algebraictopology topics. Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...
branches of topology, including differential topology, geometric topology, and algebraictopology. The fundamental concepts in point-set topology are continuity...
algebra, an interior algebra is a certain type of algebraic structure that encodes the idea of the topological interior of a set. Interior algebras are...
In mathematics, combinatorial topology was an older name for algebraictopology, dating from the time when topological invariants of spaces (for example...
axioms. For algebraic invariants see algebraictopology. For any algebraic objects we can introduce the discrete topology, under which the algebraic operations...
In mathematics, specifically in homology theory and algebraictopology, cohomology is a general term for a sequence of abelian groups, usually one associated...
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...
the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered around...
important invariants in algebraictopology. In practice, there are technical difficulties in using homotopies with certain spaces. Algebraic topologists work...
the underlying methods—differential geometry, algebraic geometry, computational geometry, algebraictopology, discrete geometry (also known as combinatorial...
equivalently, a single (continuous) path in Z Y {\displaystyle Z^{Y}} . In algebraictopology, currying serves as an example of Eckmann–Hilton duality, and, as...
captured algebraically, differential topology has strong links to algebraictopology. The central goal of the field of differential topology is the classification...
discontinuous Sheaf space Topology glossary List of topology topics List of geometric topology topics List of algebraictopology topics Publications in topology...
space or scheme. In algebraictopology it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry it is referred...
In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...
universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...
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