Space Mathematics Wikipedia

Space (mathematics) - Wikipedia.

In ancient Greek mathematics, "space" was a geometric abstraction of the three-dimensional reality observed in everyday life. About 300 BC, Euclid gave axioms for the properties of space. Euclid built all of mathematics on these geometric foundations, going so far as to define numbers by comparing the lengths of line segments to the length of a chosen reference segment..

https://en.wikipedia.org/wiki/Space_(mathematics).

Compact space - Wikipedia.

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "holes" or "missing endpoints", i.e. that the space not exclude any "limiting values" of points. For example, the "unclosed" interval (0,1) would not be compact because it excludes ....

https://en.wikipedia.org/wiki/Compact_space.

Probability space - Wikipedia.

A probability space is a mathematical triplet (,,) that presents a model for a particular class of real-world situations. As with other models, its author ultimately defines which elements , , and will contain.. The sample space is the set of all possible outcomes. An outcome is the result of a single execution of the model. Outcomes may be states of nature, possibilities, experimental ....

https://en.wikipedia.org/wiki/Probability_space.

Curvature - Wikipedia.

In mathematics, curvature is any of several strongly related concepts in geometry.Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius.Smaller circles bend more sharply, and hence have higher ....

https://en.wikipedia.org/wiki/Curvature.

Locally compact space - Wikipedia.

In topology and related branches of mathematics, a topological space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space.More precisely, it is a topological space in which every point has a compact neighborhood.. In mathematical analysis locally compact spaces that are Hausdorff are of particular interest; ....

https://en.wikipedia.org/wiki/Locally_compact_space.

List - Wikipedia.

People. List (surname) Organizations. List College, an undergraduate division of the Jewish Theological Seminary of America; SC Germania List, German rugby union club; Other uses. Angle of list, the leaning to either port or starboard of a ship; List (abstract data type) List on Sylt, previously called List, the northernmost village in Germany, on the island of Sylt.

https://en.wikipedia.org/wiki/List.

sRGB - Wikipedia.

sRGB is a standard RGB (red, green, blue) color space that HP and Microsoft created cooperatively in 1996 to use on monitors, printers, and the World Wide Web. It was subsequently standardized by the International Electrotechnical Commission (IEC) as IEC 61966-2-1:1999. sRGB is the current defined standard colorspace for the web, and it is usually the assumed ....

https://en.wikipedia.org/wiki/SRGB.

Metric (mathematics) - Wikipedia.

In mathematics, a metric or distance function is a function that gives a distance between each pair of point elements of a set.A set with a metric is a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is a metrizable space.. One important source of metrics in ....

https://en.wikipedia.org/wiki/Metric_(mathematics).

Face (geometry) - Wikipedia.

Polygonal face. In elementary geometry, a face is a polygon on the boundary of a polyhedron. Other names for a polygonal face include polyhedron side and Euclidean plane tile.. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope.With this meaning, the 4-dimensional ....

https://en.wikipedia.org/wiki/Face_(geometry).

Space Shuttle orbiter - Wikipedia.

The Space Shuttle orbiter is the spaceplane component of the Space Shuttle, a partially reusable orbital spacecraft system that was part of the discontinued Space Shuttle program.Operated from 1977 to 2011 by NASA, the U.S. space agency, this vehicle could carry astronauts and payloads into low Earth orbit, perform in-space operations, then re-enter the atmosphere and land as a ....

https://en.wikipedia.org/wiki/Space_Shuttle_orbiter.

Surjective function - Wikipedia.

In mathematics, a surjective function (also known as surjection, or onto function) is a function f that maps an element x to every element y; that is, for every y, there is an x such that f(x) = y.In other words, every element of the function's codomain is the image of at least one element of its domain. It is not required that x be unique; the function f may map one or more elements of X ....

https://en.wikipedia.org/wiki/Surjective_function.

Reflection (mathematics) - Wikipedia.

In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. For example the mirror image of the small Latin ....

https://en.wikipedia.org/wiki/Reflection_(mathematics).

Homogeneous coordinates - Wikipedia.

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Mobius in his 1827 work Der barycentrische Calcul, are a system of coordinates used in projective geometry, just as Cartesian coordinates are used in Euclidean geometry.They have the advantage that the coordinates of points, including points at infinity, can be represented using ....

https://en.wikipedia.org/wiki/Homogeneous_coordinates.

Support (mathematics) - Wikipedia.

In mathematics, the support of a real-valued function is the subset of the domain containing the elements which are not mapped to zero. If the domain of is a topological space, the support of is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis.

https://en.wikipedia.org/wiki/Support_(mathematics).

Discrete space - Wikipedia.

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a 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, every singleton subset is ....

https://en.wikipedia.org/wiki/Discrete_space.

Locally connected space - Wikipedia.

For the non-trivial direction, assume is weakly locally connected. To show it is locally connected, it is enough to show that the connected components of open sets are open.. Let be open in and let be a connected component of . Let be an element of . Then is a neighborhood of so that there is a connected neighborhood of contained in . Since is connected and contains , must be a subset ....

https://en.wikipedia.org/wiki/Locally_connected_space.

Half-space (geometry) - Wikipedia.

In geometry, a half-space is either of the two parts into which a plane divides the three-dimensional Euclidean space.If the space is two-dimensional, then a half-space is called a half-plane (open or closed). A half-space in a one-dimensional space is called a half-line or ray.. More generally, a half-space is either of the two parts into which a hyperplane divides an affine space..

https://en.wikipedia.org/wiki/Half-space_(geometry).

Orientation (vector space) - Wikipedia.

Definition. Let V be a finite-dimensional real vector space and let b 1 and b 2 be two ordered bases for V.It is a standard result in linear algebra that there exists a unique linear transformation A : V -> V that takes b 1 to b 2.The bases b 1 and b 2 are said to have the same orientation (or be consistently oriented) if A has positive determinant; otherwise they have opposite orientations..

https://en.wikipedia.org/wiki/Orientation_(vector_space).

Uniform distribution - Wikipedia.

Uniform distribution may refer to: . Continuous uniform distribution; Discrete uniform distribution; Uniform distribution (ecology) Equidistributed sequence; See also. All pages with titles containing uniform distribution; Homogeneous distribution.

https://en.wikipedia.org/wiki/Uniform_distribution.

Treasure - Wikipedia.

A treasure map is a variation of a map to mark the location of buried treasure, a lost mine, a valuable secret or a hidden location.One of the earliest known instances of a document listing buried treasure is the copper scroll, which was recovered among the Dead Sea Scrolls near Qumran in 1952. More common in fiction than in reality, "pirate treasure maps" are often ....

https://en.wikipedia.org/wiki/Treasure.