Topology


Topic | v1 | created by janarez |
Description

In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property.


Relations

relates to Homology

In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abe...

a tool for Topological data analysis (TDA)

In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets us...


Edit topic New topic

Resources

No beginner resources matching your criteria have been registered, yet.

No intermediate resources matching your criteria have been registered, yet.

No advanced resources matching your criteria have been registered, yet.

No unrated resources matching your criteria have been registered, yet.