are commonly used in the context of topology. If the set X {\displaystyle X} is a topological space, then a cover C {\displaystyle C} of X {\displaystyle...

In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies...

areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric...

structure-preserving fashion Cover (topology), the mathematical concept of a collection of sets whose union contains each set as a subset Cover, a pair in the covering...

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

with a choice of Grothendieck topology is called a site. Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering...

In mathematics, a double cover or double covering may refer to: Double cover (topology), a two-to-one mapping from one topological space to another. Frequently...

dictionary. Covering may refer to: Window covering, material used to cover a window Cover (topology), a collection of subsets of X {\displaystyle X} whose union...

In mathematics, the lower limit topology or right half-open interval topology is a topology defined on R {\displaystyle \mathbb {R} } , the set of real...

Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe...

general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It...

faces. Bott, Raoul; Tu, Loring (1982), Differential Forms in Algebraic Topology, New York: Springer, ISBN 0-387-90613-4, §5, S. 42. Weil, Andre (1952)...

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean...

topology τ of a topological space (X, τ) is a family B {\displaystyle {\mathcal {B}}} of open subsets of X such that every open set of the topology is...

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...

and topology can be drawn, however, as discussed below.[clarification needed] It is also the title of a journal Geometry & Topology that covers these...

). The sets in P are said to exhaust or cover X. See also collectively exhaustive events and cover (topology). The intersection of any two distinct sets...

circles of the rose are called petals. Roses are important in algebraic topology, where they are closely related to free groups. A rose is a wedge sum of...

In topology, a subbase (or subbasis, prebase, prebasis) for a topological space X {\displaystyle X} with topology τ {\displaystyle \tau } is a subcollection...

certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular...

geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the...

In topology, a coherent topology is a topology that is uniquely determined by a family of subspaces. Loosely speaking, a topological space is coherent...

Homotopy Path (topology) Fundamental group Homotopy group Seifert–van Kampen theorem Pointed space Winding number Simply connected Universal cover Monodromy...

In the mathematical field of topology, a uniform space is a set with additional structure that is used to define uniform properties, such as completeness...

In topology, an Alexandrov topology is a topology in which the intersection of every family of open sets is open. It is an axiom of topology that the...

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a...

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

which is a cover on Zariski open subsets. In the fpqc topology, any faithfully flat and quasi-compact morphism is a cover. These topologies are closely...

(mathematics) Continuity (topology) Homeomorphism Local homeomorphism Open and closed maps Germ (mathematics) Base (topology), subbase Open cover Covering space...

for the natural topology. The simplest cases (which nevertheless cover many examples) are the initial topology and the final topology (Willard (1970))...