Strong Local Homogeneity and Coset Spaces
نویسندگان
چکیده
We prove that for every homogeneous and strongly locally homogeneous separable metrizable space X there is a metrizable compactification γX of X such that, among other things, for all x, y ∈ X there is a homeomorphism f : γX → γX such that f(x) = y. This implies that X is a coset space of some separable metrizable topological group G.
منابع مشابه
Some relations between $L^p$-spaces on locally compact group $G$ and double coset $Ksetminus G/H$
Let $H$ and $K$ be compact subgroups of locally compact group $G$. By considering the double coset space $Ksetminus G/H$, which equipped with an $N$-strongly quasi invariant measure $mu$, for $1leq pleq +infty$, we make a norm decreasing linear map from $L^p(G)$ onto $L^p(Ksetminus G/H,mu)$ and demonstrate that it may be identified with a quotient space of $L^p(G)$. In addition, we illustrate t...
متن کاملExact duality transformations for sigma models and gauge theories
We present an exact duality transformation in the framework of Statistical Mechanics for various lattice models with non-Abelian global or local symmetries. The transformation applies to sigma models with variables in a compact Lie group G with global G×G-symmetry (the chiral model) and with variables in coset spaces G/H and a global G-symmetry (for example, the non-linear O(N) or RPN models) i...
متن کاملNon - local charges , Z m gradings and coset space actions
The construction of flat currents, and hence conserved non-local charges, for the superstring on AdS5 × S 5 is generalised. It is shown that such currents exist for sigma-model type actions on all coset (super-)spaces G/H in which, at the level of the Lie algebras, h is the grade-zero subspace of a Zm-grading of g. This is true for an essentially unique choice of the Wess-Zumino term, which is ...
متن کاملSuper coset space geometry
Super coset spaces play an important role in the formulation of supersymmetric theories. The aim of this paper is to review and discuss the geometry of super coset spaces with particular focus on the way the geometrical structures of the super coset space G/H are inherited from the super Lie group G. The isometries of the super coset space are discussed and a definition of Killing supervectors ...
متن کاملDimensional Reduction over Coset Spaces and Supersymmetry Breaking
We address the question of supersymmetry breaking of a higher dimensional supersymmetric theory due to coset space dimensional reduction. In particular we study a ten-dimensional supersymmetric E8 gauge theory which is reduced over all six-dimensional coset spaces. We find that the original supersymmetry is completely broken in the process of dimensional reduction when the coset spaces are symm...
متن کامل