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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 ...
The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. This is a list of topology topics. See also: Topology glossary; List of topologies; List of general topology topics; List of geometric topology topics
The honeycomb is a well-known example of tessellation in nature with its hexagonal cells. [82] In botany, the term "tessellate" describes a checkered pattern, for example on a flower petal, tree bark, or fruit. Flowers including the fritillary, [83] and some species of Colchicum, are characteristically tessellate. [84]
The art reporter Jonathan Keats, writing in ForbesLife, argues that Man Ray photographed "the elliptic paraboloids and conic points in the same sensual light as his pictures of Kiki de Montparnasse", and "ingeniously repurposes the cool calculations of mathematics to reveal the topology of desire". [128]
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
Continuum (topology) Extended real number line; Long line (topology) Sierpinski space; Cantor set, Cantor space, Cantor cube; Space-filling curve; Topologist's sine curve; Uniform norm; Weak topology; Strong topology; Hilbert cube; Lower limit topology; Sorgenfrey plane; Real tree; Compact-open topology; Zariski topology; Kuratowski closure ...
This is a list of useful examples in general topology, a field of mathematics. Alexandrov topology; Cantor space; Co-kappa topology Cocountable topology; Cofinite topology; Compact-open topology; Compactification; Discrete topology; Double-pointed cofinite topology; Extended real number line; Finite topological space; Hawaiian earring; Hilbert cube
Examples of closed surfaces include the sphere, the torus and the Klein bottle. Examples of non-closed surfaces include an open disk (which is a sphere with a puncture), a cylinder (which is a sphere with two punctures), and the Möbius strip. A surface embedded in three-dimensional space is closed if and only if it is the boundary of a solid.