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1. 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. (Branch of mathematics) [100%] 2023-11-05 [Algebraic topology]
2. Algebraic topology: The branch of mathematics in which one studies such properties of geometrical figures (in a wider sense, of all objects for which one can speak of continuity), and their mappings into each other, which remain unchanged under continuous deformations (homotopies ... (Mathematics) [100%] 2023-10-28
3. 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. (Branch of mathematics) [100%] 2023-06-07 [Algebraic topology]
4. Algebraic topology: Algebraic topology is a branch of mathematics that uses abstract algebra to understand topological spaces, and topology to understand abstract algebra. The primary method of algebraic topology is to identify some kind of relation between a group (or a ring ... [100%] 2023-02-22 [Topology] [Algebra]...
5. Algebraic topology (object): In mathematics, the algebraic topology on the set of group representations from G to a topological group H is the topology of pointwise convergence, i.e. pi converges to p if the limit of pi(g) = p(g) for every ... (Object) [100%] 2023-04-11 [3-manifolds] [Algebraic topology]...
6. Algebraic algebra: An algebra with associative powers (in particular, an associative algebra) over a field in which all elements are algebraic: an element $a$ of the algebra $A$ is called algebraic over the field $F$ if the subalgebra $F$ generated by $a ... (Mathematics) [83%] 2023-10-13
7. Directed algebraic topology: In mathematics, directed algebraic topology is a refinement of algebraic topology for directed spaces, topological spaces and their combinatorial counterparts equipped with some notion of direction. Some common examples of directed spaces are spacetimes and simplicial sets. [81%] 2023-12-27 [Algebraic topology]
8. Quantum Algebraic Topology: Quantum Algebraic Topology is a theoretical subfield of quantum physics focused on quantum operator algebra and topology of quantum spaces. Both topological quantum field theory and noncommutative geometry may be considered related fields. [81%] 2023-03-03 [Topology]
9. Nonabelian algebraic topology: In mathematics, nonabelian algebraic topology studies an aspect of algebraic topology that involves (inevitably noncommutative) higher-dimensional algebras. Many of the higher-dimensional algebraic structures are noncommutative and, therefore, their study is a very significant part of nonabelian category theory ... [81%] 2024-06-23 [Algebraic topology]
10. Topology: Topology is a branch of advanced mathematics devoted to spatial relationships. It can also be described as the manipulation and mapping of sets. [72%] 2023-02-15 [Mathematics] [Topology]...
11. Topology: Topology is the natural evolution of analysis to a more general level. Whereas analysis was concerned with the implications of continuity on the familiar spaces of R and C, topology seeks to explore all the types of mathematical structures where ... [72%] 2024-01-01 [{{PAGENAME}}] [Introductions]...
12. Topology: When it comes to mathematics, topology (derived from the Greek words "o" meaning "place, location," and "study" meaning "study") is the study of the properties of a geometric object that are preserved under continuous deformations such as stretching, twisting, crumpling ... [72%] 2024-01-01 [Topology] [Mathematical structures]...
13. Topology: In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for ... (Chemistry) [72%] 2023-09-20 [Molecular topology] [Molecular geometry]...
14. Topology: Topology (from Greek τόπος - "place" and λόγος - "study") is a branch of mathematics that studies the propeties of objects that are preserved through continuous deformations (such as stretching, bending and compression). "Continuous" means that ruptures (breaking of the object's integrity) and ... [72%] 2023-08-21
15. Topology (mathematics): Topology (mathematics) : The study of spatial properties invariant under continuous deformations. (Mathematics) [72%] 2023-06-16
16. Glossary of algebraic topology: This is a glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category theory, glossary of differential geometry and topology, Timeline of manifolds. (Mathematics glossary) [70%] 2024-10-08 [Algebraic topology] [Glossaries of mathematics]...
17. Lie algebra, algebraic: The Lie algebra of an algebraic subgroup (see Algebraic group) of the general linear group of all automorphisms of a finite-dimensional vector space $V$ over a field $k$. If $\mathfrak g$ is an arbitrary subalgebra of the Lie algebra ... (Mathematics) [67%] 2023-10-17
18. Typology (theology): Typology in Christian theology and Biblical exegesis is a doctrine or theory concerning the relationship of the Old Testament to the New Testament. Events, persons, or statements in the Old Testament are seen as types pre-figuring or superseded by ... (Social) [63%] 2023-12-18
19. Typology (anthropology): Typology in anthropology was the categorization of the human species by races, based solely on traits that are readily observable from a distance such as head shape, skin color, hair form, body build, and stature. During the late 19th and ... (Social) [63%] 2023-09-21 [Anthropology]
20. Typology: Typology ("study of types") refers to the Christian concept of Old Testament scenes and characters ("type") as foreshadowing those in the New Testament ("antitype") and was a commonly used device within the broader artform of Christian iconography. It was typically ... [63%] 2023-02-16 [Art] [Bible]...