inclusion topology

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• Inclusion map — A is a subset of B, and B is a superset of A. In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, or canonical injection) is the function i that sends each element …   Wikipedia

• Geospatial topology — Topology In a Geographic Information System GIS, topology is a set of rules which define the relationship between points, lines, and polygons. ESRI enables topology generation within their geodatabase feature classes. Network topology explores… …   Wikipedia

• Grothendieck topology — In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a …   Wikipedia

• Coherent topology — In topology, a coherent topology is one that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent with a family of subspaces if it is a topological union of those subspaces. Contents 1 Definition 2… …   Wikipedia

• Subspace topology — In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a natural topology induced from that of X called the subspace topology (or the relative topology, or the induced topology …   Wikipedia

• Alexandrov topology — In topology, an Alexandrov space (or Alexandrov discrete space) is a topological space in which the intersection of any family of open sets is open. It is an axiom of topology that the intersection of any finite family of open sets is open. In an …   Wikipedia

• Closure (topology) — For other uses, see Closure (disambiguation). In mathematics, the closure of a subset S in a topological space consists of all points in S plus the limit points of S. Intuitively, these are all the points that are near S. A point which is in the… …   Wikipedia

• Initial topology — In general topology and related areas of mathematics, the initial topology (projective topology or weak topology) on a set X, with respect to a family of functions on X, is the coarsest topology on X which makes those functions continuous.The… …   Wikipedia

• Natural topology — In any domain of mathematics, a space has a natural topology if there is a topology on the space which is best adapted to its study within the domain in question. In many cases this imprecise definition means little more than the assertion that… …   Wikipedia

• Zariski topology — In algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition. It is due to Oscar Zariski and took a place of particular importance in the field around… …   Wikipedia

• Final topology — In general topology and related areas of mathematics, the final topology (inductive topology or strong topology) on a set X, with respect to a family of functions into X, is the finest topology on X which makes those functions continuous.… …   Wikipedia