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...

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

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...

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...

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

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...

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

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...

worked in geometric topology, both in high dimensions, relating pseudoisotopy to algebraic K-theory, and in low dimensions: surfaces and 3-manifolds, such...

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

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

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...

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

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

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

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

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

triangulations established a new branch in topology, namely the piecewise-linear-topology (short PL-topology). Its main purpose is topological properties...

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

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...

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...

In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain sense "longer". It behaves...

infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in a solid ball...

to generate their subdivision procedure to produce C1 limit surfaces with arbitrary topology for arbitrary initial meshes. An auxiliary point can improve...

In topology, especially algebraic topology, the cone of a topological space X {\displaystyle X} is intuitively obtained by stretching X into a cylinder...

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...

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

from point-set topology, classic algebraic topology, and geometric topology. The most familiar invariants, which are visible for surfaces, are orientability...

gap-to-sample-area ratio may cause uneven distribution of current and affect the surface topology of the plated sample. Stirring may increase the transfer/diffusion...