In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional...

Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric...

study of topology. In 1827, Carl Friedrich Gauss published General investigations of curved surfaces, which in section 3 defines the curved surface in a similar...

number of "holes" of a surface. A sphere has genus 0, while a torus has genus 1. The genus of a connected, orientable surface is an integer representing...

differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct...

geometry, a surface may cross itself (and may have other singularities), while, in topology and differential geometry, it may not. A surface is a topological...

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points in the closure of S not belonging to the...

Clifford torus, a surface in 4-space. In the field of topology, a torus is any topological space that is homeomorphic to a torus. The surface of a coffee cup...

by having a low grooving surface. Besides friction, low grooving surfaces depend on the topology (surface) factors of surface texture (lay) and spacing...

Jost, (1997) "Compact Riemann Surfaces: An Introduction to Contemporary Mathematics", Springer James R. Munkres, Topology, Second Edition, Prentice-Hall...

some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise"...

manifold Surface (topology), a two-dimensional manifold Algebraic surface, an algebraic variety of dimension two Coordinate surfaces Fractal surface, generated...

In mathematics, and more precisely in topology, the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group,...

geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Geometric topology as an area...

Computer Atlas of Surface Topography of Proteins (CASTp) aims to provide comprehensive and detailed quantitative characterization of topographic features...

of triangulations established a new branch in topology, namely piecewise linear topology (or PL topology). Its main purpose is to study the topological...

This is a list of geometric topology topics. Knot (mathematics) Link (knot theory) Wild knots Examples of knots (and links) Unknot Trefoil knot Figure-eight...

for some commonly used materials are listed in the table below. The surface topology of the electrode plays an important role in determining the efficiency...

José da Costa. It is also a surface of finite topology, which means that it can be formed by puncturing a compact surface. Topologically, it is a thrice-punctured...

minimal surface with the topology of the Möbius strip, can be constructed using solutions to the Björling problem, which defines a minimal surface uniquely...

"A presentation for the mapping class group of a closed orientable surface". Topology. 19 (3): 221–237. doi:10.1016/0040-9383(80)90009-9. Imayoshi, Yôichi;...

topological insulators, spin-split surface states exist independently from the Rashba effect, due to the surface topology. Topological insulators display...

In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions...

using methods from computable topology. A large family of algorithms concerning 3-manifolds revolve around normal surface theory, which is a phrase that...

digital topology are used to specify and justify important (low-level) image analysis algorithms, including algorithms for thinning, border or surface tracing...

In topology, a branch of mathematics, a lamination is a : "topological space partitioned into subsets" decoration (a structure or property at a point)...

characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It...

often called a surface bundle over the circle. Mapping torus Salter, Nick; Tshishiku, Bena (21 October 2019). "Surface bundles in topology, algebraic geometry...

primarily by its curvature, while the global geometry is characterised by its topology (which itself is constrained by curvature). General relativity explains...

In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of...