Discrete space - Wikipedia

Discrete space - Wikipedia: "the finest topology that can be given on a set, i.e., it defines all subsets as open sets."



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Topological space - Wikipedia

Topological space - Wikipedia: "define a subset U of X to be open if U is a neighbourhood of all points in U."



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Irrational number - Wikipedia

Irrational number - Wikipedia: "When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself."



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Symmetric space - Wikipedia

Symmetric space - Wikipedia: "a symmetric space is the quotient G/H of Lie group G by a Lie subgroup H, "



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Symmetry breaking - Wikipedia

Symmetry breaking - Wikipedia:



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Topological group - Wikipedia

Topological group - Wikipedia: "the topology on G be Hausdorff; it is equivalent to assume that the identity element 1 is a closed subset of G."



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Quotient space (topology) - Wikipedia

Quotient space (topology) - Wikipedia: "In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given topological space."



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Orbit - Encyclopedia of Mathematics

Orbit - Encyclopedia of Mathematics: "The orbits of any two points from either do not intersect or coincide"



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Special linear group - Wikipedia

Special linear group - Wikipedia: "this corresponds to the interpretation of the determinant as measuring change in volume and orientation"



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Equivariant map - Wikipedia

Equivariant map - Wikipedia: "Equivariant maps generalize the concept of invariants"



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Groups for Dummies

Groups for Dummies: "an n x n matrix has n eigenvalues, and they are invariant under a similarity transformation. ... The determinant is the product of all n eigenvalues, and the trace is their sum."



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Space (mathematics) - Wikipedia

Space (mathematics) - Wikipedia: " The open interval {\displaystyle (0,1)} is homeomorphic to the whole real line {\displaystyle (-\infty ,\infty )} but not homeomorphic to the closed interval {\displaystyle [0,1]} , nor to a circle."



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Form - Encyclopedia of Mathematics

Form - Encyclopedia of Mathematics: "they are called linear (for n=1n=1), quadratic (for n=2n=2), cubic (for n=3n=3), etc."



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Box topology - Wikipedia

Box topology - Wikipedia: "In particular, if all the component spaces are compact, the box topology on their Cartesian product will not necessarily be compact, although the product topology on their Cartesian product will always be compact."



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