22 relations: Aleksandr Danilovich Aleksandrov, Alexandrov topology, Base (topology), Causal structure, Comparison of topologies, Curvature, Dimension, General relativity, Gravitational singularity, Gravity, Hausdorff space, Locally compact space, Manifold, Open set, Pavel Alexandrov, Physical cosmology, Pseudo-Riemannian manifold, Separable space, Spacetime, Theoretical physics, Topological space, Topology.
Aleksandr Danilovich Aleksandrov
Aleksandr Danilovich Aleksandrov (Алекса́ндр Дани́лович Алекса́ндров, alternative transliterations: Alexandr or Alexander (first name), and Alexandrov (last name)) (August 4, 1912 – July 27, 1999), was a Soviet/Russian mathematician, physicist, philosopher and mountaineer.
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Alexandrov topology
In topology, an Alexandrov topology is a topology in which the intersection of any family of open sets is open.
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Base (topology)
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.We are using a convention that the union of empty collection of sets is the empty set.
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Causal structure
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
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Comparison of topologies
In topology and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set.
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Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
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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.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Gravitational singularity
A gravitational singularity or spacetime singularity is a location in spacetime where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system.
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Gravity
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.
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Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods.
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Locally compact space
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.
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Open set
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
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Pavel Alexandrov
Pavel Sergeyevich Alexandrov (Па́вел Серге́евич Алекса́ндров), sometimes romanized Paul Alexandroff or Aleksandrov (7 May 1896 – 16 November 1982), was a Soviet mathematician.
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Physical cosmology
Physical cosmology is the study of the largest-scale structures and dynamics of the Universe and is concerned with fundamental questions about its origin, structure, evolution, and ultimate fate.
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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
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Separable space
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence \_^ of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Redirects here:
Global geometry, Global spacetime structure, Spacetime Topology, Spacetime manifold, Universal Topology of Physics.
References
[1] https://en.wikipedia.org/wiki/Spacetime_topology