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# Point (geometry)

In modern mathematics, a point refers usually to an element of some set called a space. [1]

54 relations: Affine space, Alfred North Whitehead, Algebra of sets, Area, Axiom, Boundary (topology), C*-algebra, Classical electromagnetism, Complete Heyting algebra, Continuous function, Convention (norm), Cover (topology), Critical point (mathematics), Cusp (singularity), Degeneracy (mathematics), Dimension, Element (mathematics), Euclid, Euclidean geometry, Euclidean space, Foundations of geometry, Function (mathematics), Generalized function, Horizontal plane, Infimum and supremum, Infinity, Integral, Kronecker delta, Length, Limit point, Line (geometry), Line segment, Linear independence, Mathematics, Metric space, Noncommutative geometry, Ordered pair, Paul Dirac, Plane (geometry), Point particle, Pointless topology, Pointwise, Position (vector), Primitive notion, Process and Reality, Set (mathematics), Signal processing, Singular point of a curve, Space (mathematics), Trinity College, Cambridge, ... Expand index (4 more) »

## Affine space

In mathematics, an affine space is a geometric structure that generalizes certain properties of parallel lines in Euclidean space.

Alfred North Whitehead, OM FRS (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

## Algebra of sets

The algebra of sets defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

## Axiom

An axiom or postulate is a premise or starting point of reasoning.

## Boundary (topology)

In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. The term boundary operation refers to finding or taking the boundary of a set.

## C*-algebra

C&lowast;-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics.

## Classical electromagnetism

Classical electromagnetism (or classical electrodynamics) is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.

## Complete Heyting algebra

In mathematics, especially in order theory, a complete Heyting algebra is a Heyting algebra that is complete as a lattice.

## Continuous function

In mathematics, a continuous function is, roughly speaking, a function for which small changes in the input result in small changes in the output.

## Convention (norm)

A convention is a set of agreed, stipulated, or generally accepted standards, norms, social norms, or criteria, often taking the form of a custom.

## Cover (topology)

In mathematics, a cover of a set X is a collection of sets whose union contains X as a subset.

## Critical point (mathematics)

In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0 or undefined.

## Cusp (singularity)

In the mathematical theory of singularities a cusp is a type of singular point of a curve.

## Degeneracy (mathematics)

In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class.

## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

## Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry".

## Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Foundations of geometry

Foundations of geometry is the study of geometries as axiomatic systems.

## Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

## Generalized function

In mathematics, generalized functions, or distributions, are objects extending the notion of functions.

## Horizontal plane

In geometry, physics, astronomy, geography, and related sciences, a plane is said to be horizontal at a given point if it is perpendicular to the gradient of the gravity field at that point&mdash; in other words, if apparent gravity makes a plumb bob hang perpendicular to the plane at that point.

## Infimum and supremum

In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element that is less than or equal to all elements of S, if such an element exists.

## Infinity

Infinity (symbol) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.

## Integral

The integral is an important concept in mathematics.

## Kronecker delta

In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker, is a function of two variables, usually just positive integers.

## Length

In geometric measurements, length is the most extended dimension of an object.

## Limit point

In mathematics, a limit point of a set S in a topological space X is a point x (which is in X, but not necessarily in S) that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.

## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its end points.

## Linear independence

In the theory of vector spaces the concept of linear dependence and linear independence of the vectors in a subset of the vector space is central to the definition of dimension.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## Noncommutative geometry

Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of spaces that are locally presented by noncommutative algebras of functions (possibly in some generalized sense).

## Ordered pair

In mathematics, an ordered pair (a, b) is a pair of mathematical objects.

## Paul Dirac

Paul Adrien Maurice Dirac (8 August 1902 – 20 October 1984) was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface.

## Point particle

A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics.

## Pointless topology

In mathematics, pointless topology (also called point-free or pointfree topology) is an approach to topology that avoids mentioning points.

## Pointwise

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some function f. An important class of pointwise concepts are the pointwise operations &mdash; operations defined on functions by applying the operations to function values separately for each point in the domain of definition.

## Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line distance from O to P: The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally in vector calculus.

## Primitive notion

In mathematics, logic, and formal systems, a primitive notion is an undefined concept.

## Process and Reality

Process and Reality is a book by Alfred North Whitehead, in which he propounds a philosophy of organism, also called process philosophy.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Signal processing

Signal processing is an enabling technology that encompasses the fundamental theory, applications, algorithms, and implementations of processing or transferring information contained in many different physical, symbolic, or abstract formats broadly designated as signals.

## Singular point of a curve

In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.

## Space (mathematics)

In mathematics, a space is a set (sometimes called a universe) with some added structure.

## Trinity College, Cambridge

Trinity College is a constituent college of the University of Cambridge in England.

## Tuple

A tuple is a finite ordered list of elements.

## Vertical direction

In astronomy, geography, geometry and related sciences and contexts, a direction passing by a given point is said to be vertical if it is locally aligned with the gradient of the gravity field, i.e., with the direction of the gravitational force (per unit mass, i.e. gravitational acceleration vector) at that point.

## Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.

## Zero-dimensional space

In mathematics, a zero-dimensional topological space (or nildimensional) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.

## References

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