Topology Topology In mathematics, specifically topology, a covering map on a topological space X is a continuous surjective map p : C → X, with C another topological space, with the property that for every x in X there exists an open neighborhood U such that the inverse image of U under p is a union of mutually disjoint open sets each of which is mapped homeomorphically onto U by p. ...more on Wikipedia about "Covering map"
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. Simple examples are the circle or the straight line. A large number of other curves have been studied in geometry. ...more on Wikipedia about "Curve"
In mathematics, a deformation retract in topology is a map which captures the idea of continuously shrinking a space into a subspace. ...more on Wikipedia about "Deformation retract"
In abstract algebra, a derivative algebra is an algebraic structure of the signature ...more on Wikipedia about "Derivative algebra (abstract algebra)"
In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of 'gluing' in topology. Since the topologists' glue is actually the use of equivalence relations on topological spaces, the theory starts with some ideas on identification. ...more on Wikipedia about "Descent (category theory)"
In topology and related fields of mathematics, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense. ...more on Wikipedia about "Discrete space"
In topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. ...more on Wikipedia about "Disjoint union (topology)"
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In mathematics, an Fσ set (said F-sigma set) is a countable union of closed sets. The notation originated in France with F for fermé ( French:closed) and σ for somme (French:union). ...more on Wikipedia about "F-sigma set"
In topology and related areas of mathematics, the final topology (inductive topology or strong topology) on a set , with respect to a family of functions into , is the finest topology on X which makes those functions continuous. ...more on Wikipedia about "Final topology"
In mathematics, the fixed point index is a concept in topological fixed point theory, and in particular Nielsen theory. The fixed point index can be thought of as a multiplicity measurement for fixed points. ...more on Wikipedia about "Fixed point index"
In the mathematical field of topology a G-delta set or Gδ set is a set in a topological space which is in a certain sense simple. The notation originated in Germany with G for Gebiet ( German:area) meaning open set in this case and δ for Durchschnitt (german: intersection). ...more on Wikipedia about "G-delta set"
In topology and related areas of mathematics a gauge space is a topological space where the topology is defined by a family of pseudometrics. ...more on Wikipedia about "Gauge space"
In mathematics, genus has a few different, but closely related, meanings: ...more on Wikipedia about "Genus (mathematics)"
In mathematics, geometric topology is the study of manifolds and their embeddings, with representative topics being knot theory and braid groups. It has come over time to be almost synonymous with low-dimensional topology, concerning in particular manifolds of less than five dimensions. ...more on Wikipedia about "Geometric topology"
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In mathematics, a germ is an equivalence class of continuous functions from one topological space to another (often from the real line to itself), in which one point x0 in the domain has been singled out as privileged. Two functions f and g are equivalent precisely if there is some open neighborhood U of x0 such that for all x ∈ U, the identity f(x) = g(x) holds. All local properties of f at x0 depend only on which germ f belongs to. ...more on Wikipedia about "Germ (mathematics)"
A graph also admits a natural topology, called the graph topology, by identifying every edge with the unit interval and gluing them together at coincident vertices. ...more on Wikipedia about "Graph topology"
The hairy ball theorem of algebraic topology states that, in layman's terms, "one cannot comb the hair on a ball in a smooth manner". ...more on Wikipedia about "Hairy ball theorem"
In measure theory, a branch of mathematics, the ham sandwich theorem, also called the Stone-Tukey theorem after Marshall Stone and John Tukey, states that given n "objects" in n- dimensional space, it is possible to divide each one in half (according to volume) with a single (n − 1)-dimensional hyperplane. Here the "objects" should be sets of finite measure (or, in fact, just of finite outer measure) for the notion of "dividing the volume in half" to make sense. ...more on Wikipedia about "Ham sandwich theorem"
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which points can be separated by neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the Hausdorff condition is the most frequently used and discussed . ...more on Wikipedia about "Hausdorff space"
In mathematical analysis, the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: ...more on Wikipedia about "Heine–Borel theorem"
In mathematics, the Hilbert-Smith conjecture is concerned with the transformation groups of manifolds; and in particular with the limitations on topological groups G that can act effectively (faithfully) on a (topological) manifold M. Restricting to G which are locally compact and have a continuous, faithful group action on M, it states that G must be a Lie group. ...more on Wikipedia about "Hilbert-Smith conjecture"
In the mathematical field of topology a homeomorphism or topological isomorphism (from the Greek words homeos = identical and morphe = shape) is a special isomorphism between topological spaces which respects topological properties. Two spaces with a homeomorphism between them are called homeomorphic. From a topological viewpoint they are the same. ...more on Wikipedia about "Homeomorphism"
In mathematics, the homotopy category of topological spaces, often denoted hTop or Toph, is the category whose objects are topological spaces and whose morphisms are homotopy equivalence classes of continuous maps. This is a category because the homotopy relation is compatible with function composition in the following sense: if ...more on Wikipedia about "Homotopy category of topological spaces"
In topology and related areas of mathematics, the initial topology (projective topology or weak topology) on a set , with respect to a family of functions on , is the coarsest topology on X which makes those functions continuous. ...more on Wikipedia about "Initial topology"
In mathematics, interval is a concept relating to the sequence and set-membership of one or more numbers. ...more on Wikipedia about "Interval (mathematics)" You are visiting www.shortopedia.com
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