Table of Contents
14 relations: Abelian group, Cartesian product, Circle group, Compact space, Connected space, Disk (mathematics), Duocylinder, Inverse limit, Mathematics, Pontryagin duality, Proprism, Solenoid (mathematics), Topological abelian group, Torus.
Abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
See Protorus and Abelian group
Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets and, denoted, is the set of all ordered pairs where is in and is in.
See Protorus and Cartesian product
Circle group
In mathematics, the circle group, denoted by \mathbb T or, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers \mathbb T.
Compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.
See Protorus and Compact space
Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets.
See Protorus and Connected space
Disk (mathematics)
In geometry, a disk (also spelled disc).
See Protorus and Disk (mathematics)
Duocylinder
The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is similar to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.
Inverse limit
In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the precise gluing process being specified by morphisms between the objects.
See Protorus and Inverse limit
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Pontryagin duality
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), the finite abelian groups (with the discrete topology), and the additive group of the integers (also with the discrete topology), the real numbers, and every finite-dimensional vector space over the reals or a p-adic field.
See Protorus and Pontryagin duality
Proprism
In geometry of 4 dimensions or higher, a proprism is a polytope resulting from the Cartesian product of two or more polytopes, each of two dimensions or higher.
Solenoid (mathematics)
In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each S_i is a circle and fi is the map that uniformly wraps the circle S_ for n_ times (n_ \geq 2) around the circle S_i. Protorus and solenoid (mathematics) are topological groups.
See Protorus and Solenoid (mathematics)
Topological abelian group
In mathematics, a topological abelian group, or TAG, is a topological group that is also an abelian group. Protorus and topological abelian group are topological groups.
See Protorus and Topological abelian group
Torus
In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.
References
Also known as Pro-torus.