Some definitions that may be useful
... set = Functors(G → set) Yoneda’s lemma: We have a full faithful embedding Gop ,→ G set. It sends ? 7→ Hom(?, −) = G G = G with its left multiplication action, and g 7→ left multiplication by g. The content of Yoneda’s lemma is that End(G G) = Gop = G acting on the right. (Yoneda’s lemma)2 : We have ...
... set = Functors(G → set) Yoneda’s lemma: We have a full faithful embedding Gop ,→ G set. It sends ? 7→ Hom(?, −) = G G = G with its left multiplication action, and g 7→ left multiplication by g. The content of Yoneda’s lemma is that End(G G) = Gop = G acting on the right. (Yoneda’s lemma)2 : We have ...
1. R. F. Arens, A topology for spaces of transformations, Ann. of Math
... property. Nevertheless, complete metric algebras have it. We append this section to consider such matters. For greater generality, define an m-ring as a ring whose elements form a metrizable topological group under addition, and whose product is continuous in each factor, under the topology. T H E O ...
... property. Nevertheless, complete metric algebras have it. We append this section to consider such matters. For greater generality, define an m-ring as a ring whose elements form a metrizable topological group under addition, and whose product is continuous in each factor, under the topology. T H E O ...
Affine Varieties
... Proposition 3.3: The only rational functions φ ∈ C(X) that are regular at all the points of X are the regular functions. Proof: Consider all the possible expressions for such a φ as a ratio φ = fg . The set of denominators g that occur (and 0) is an ideal Iφ ⊆ C[X] since: ...
... Proposition 3.3: The only rational functions φ ∈ C(X) that are regular at all the points of X are the regular functions. Proof: Consider all the possible expressions for such a φ as a ratio φ = fg . The set of denominators g that occur (and 0) is an ideal Iφ ⊆ C[X] since: ...
1 Dimension 2 Dimension in linear algebra 3 Dimension in topology
... Intuitively we all know what the dimension of something is supposed to be. A point is 0-dimensional, a line 1-dimesional, a plane 2-dimensional, the space we live in 3-dimensional. The dimension gives the number of free parameters, the number of coordinates needed to specify a point. Also a curved l ...
... Intuitively we all know what the dimension of something is supposed to be. A point is 0-dimensional, a line 1-dimesional, a plane 2-dimensional, the space we live in 3-dimensional. The dimension gives the number of free parameters, the number of coordinates needed to specify a point. Also a curved l ...
JORDAN ALGEBRAS OF SELF
... 1. Introduction. A Jordan algebra of self-adjoint operators on a Hubert space, or simply, a J-algebra, is a real linear space of such operators closed under the product A o B=^(AB + BA). A JC-algebra, respectively, a JW-algebra, is a uniformly closed, respectively, weakly closed /-algebra (we show i ...
... 1. Introduction. A Jordan algebra of self-adjoint operators on a Hubert space, or simply, a J-algebra, is a real linear space of such operators closed under the product A o B=^(AB + BA). A JC-algebra, respectively, a JW-algebra, is a uniformly closed, respectively, weakly closed /-algebra (we show i ...