Search results
Results from the WOW.Com Content Network
A topological algebra over a topological field is a topological vector space together with a bilinear multiplication :, (,) that turns into an algebra ...
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
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 .
A topological vector space is a topological module over a topological field. An abelian topological group can be considered as a topological module over Z , {\displaystyle \mathbb {Z} ,} where Z {\displaystyle \mathbb {Z} } is the ring of integers with the discrete topology .
It was established in 1971 as General Topology and Its Applications, and renamed to its current title in 1980. The journal currently publishes 18 issues each year in one volume. It is indexed by Scopus, Mathematical Reviews, and Zentralblatt MATH. Its 2004–2008 MCQ was 0.38 and its 2020 impact factor was 0.617. [1]
Cardinal functions are widely used in topology as a tool for describing various topological properties. [4] [5] Below are some examples.(Note: some authors, arguing that "there are no finite cardinal numbers in general topology", [6] prefer to define the cardinal functions listed below so that they never take on finite cardinal numbers as values; this requires modifying some of the definitions ...
completely determine its homology groups with coefficients in A, for any abelian group A: (,) Here might be the simplicial homology, or more generally the singular homology. The usual proof of this result is a pure piece of homological algebra about chain complexes of free abelian groups.
This corresponds also to the period where homological algebra and category theory were introduced for the study of topological spaces, and largely supplanted combinatorial methods. More recently the term combinatorial topology has been revived for investigations carried out by treating topological objects as composed of pieces as in the older ...