On resolvable spaces and groups - EMIS Home
... This section contains the relevant concepts, de nitions and results in the theory of maximal and irresolvable spaces which form the basis of our work. The following two de nitions were introduced by E. Hewitt. De nition 2.1. A space X is k-resolvable (2 k) if X contains k disjoint dense subsets. I ...
... This section contains the relevant concepts, de nitions and results in the theory of maximal and irresolvable spaces which form the basis of our work. The following two de nitions were introduced by E. Hewitt. De nition 2.1. A space X is k-resolvable (2 k) if X contains k disjoint dense subsets. I ...
HIGHER CATEGORIES 1. Introduction. Categories and simplicial
... Definition. Opposite category Cop . It has the same objects and inverted morphisms: HomCop (x, y) = HomC (y, x). Functors Cop → D are sometimes called the contravariant functors. Definition. P (C) = Fun(Cop , Set) — the category of presheaves. Here is the origin of the name. Let X be a topological s ...
... Definition. Opposite category Cop . It has the same objects and inverted morphisms: HomCop (x, y) = HomC (y, x). Functors Cop → D are sometimes called the contravariant functors. Definition. P (C) = Fun(Cop , Set) — the category of presheaves. Here is the origin of the name. Let X be a topological s ...
0OTTI-I and Ronald BROWN Let y
... Finally, (ii) follows from 16, Theorem 3.2(i)]. ,2. If B is a point, then the ex-exponential law reduces to the usual1 exposential law for pointed spaces. We know of only one circumstance when this latter exponental function is a homeomorphism, namely when X, Y are compact Hausdorff. A We saw in Sec ...
... Finally, (ii) follows from 16, Theorem 3.2(i)]. ,2. If B is a point, then the ex-exponential law reduces to the usual1 exposential law for pointed spaces. We know of only one circumstance when this latter exponental function is a homeomorphism, namely when X, Y are compact Hausdorff. A We saw in Sec ...
gb-Compactness and gb-Connectedness Topological Spaces 1
... Throughout this paper (X, τ ), (Y, σ) are topological spaces with no separation axioms assumed unless otherwise stated. Let A ⊆ X. The closure of A and the interior of A will be denoted by Cl(A) and Int(A) respectively. Definition 2.1 A subset A of X is said to be b-open [1] if A ⊆ Int(Cl(A))∪ Cl(In ...
... Throughout this paper (X, τ ), (Y, σ) are topological spaces with no separation axioms assumed unless otherwise stated. Let A ⊆ X. The closure of A and the interior of A will be denoted by Cl(A) and Int(A) respectively. Definition 2.1 A subset A of X is said to be b-open [1] if A ⊆ Int(Cl(A))∪ Cl(In ...
we defined the Poisson boundaries for semisimple Lie groups
... T h a t is, if P(G, jtx) = (£, v0), then there is an equivariant, measurable map p: B—>M such that p(*>o) =*'. In case G is a semisimple Lie group and fi is an absolutely continuous measure on G, we found in [4] that the underlying space B of P(G, /x) is a compact homogeneous space of G. In fact, it ...
... T h a t is, if P(G, jtx) = (£, v0), then there is an equivariant, measurable map p: B—>M such that p(*>o) =*'. In case G is a semisimple Lie group and fi is an absolutely continuous measure on G, we found in [4] that the underlying space B of P(G, /x) is a compact homogeneous space of G. In fact, it ...
