We show that any infinite compact Hausdorff space S is the continuous image of a totally disconnected compact Hausdorff space S', having the same topological weight as S, by a map 95 which admits a regular linear operator of averaging, i.e., a projection of norm one of C(S') onto <p°C(S), where <p°: C(S) -*■ C(S') is the isometric embedding which takes fe C(S) into/« ¡p. A corollary of this the...

We consider, for G a simply connected domain and 0 < p < ∞, the Hardy space H(G) formed by fixing a Riemann map τ of the unit disc onto G, and demanding of functions F holomorphic on G that the integrals of |F |p over the curves τ({|z| = r}) be bounded for 0 < r < 1. The resulting space is usually not the one obtained from the classical Hardy space of the unit disc by conformal mapping. This is...

A Hausdorff topological group G is minimal if every continuous isomorphism f : G → H between G and a Hausdorff topological group H is open. Clearly, every compact Hausdorff group is minimal. It is well known that every infinite compact Hausdorff group contains a non-trivial convergent sequence. We extend this result to minimal abelian groups by proving that every infinite minimal abelian group ...

We give an example of a nonsupercompaet continuous image of a supercompact space. 0. Introduction. This paper deals with supercompact spaces. A space is called supercompact (cf. de Groot [7] ) provided it has a closed subbase such that any of its linked subsystems (a system of sets is called linked if any two of its members meet) has nonempty intersection. Much work has been done to show that c...

We prove that the semigroup operation of a topological semigroup S extends to a continuous semigroup operation on its the Stone-Čech compactification βS provided S is a pseudocompact openly factorizable space, which means that each map f : S → Y to a second countable space Y can be written as the composition f = g ◦ p of an open map p : X → Z onto a second countable space Z and a map g : Z → Y ...

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply deened compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the...

Let G be any Hausdorff topological group and let βGX denote the maximal G-compactification of a G-Tychonoff space X (i.e., a Tychonoff G-space possessing a G-compactification). Recall that a completely regular Hausdorff topological space is called pseudocompact if every continuous function f : X →R is bounded. In this paper, we prove that if X and Y are two G-Tychonoff spaces such that the prod...

Kuratowski [6] showed that a continuous compact map f : X → X defined on a closed convex subset X of a Banach space has a fixed point. This theorem has enormous influence on fixed point theory, variational inequalities, and equilibrium problems. In 1968, Goebel [5] established the well-known coincidence theorem, and then there had been a lot of generalization and application (see, [1, 2, 5]). L...

Explicit product formulas are obtained for families of multivariate polynomials which are orthogonal on simplices and on a parabolic biangle in R. These product formulas are shown to give rise to measure algebras which are hypergroups. The article also includes an elementary proof that the Michael topology for the space of compact subsets of a topological space (which is used in the definition ...

Ramı́rez-Páramo proved that under GCH for the class of compact Hausdorff spaces i-weight reflects all cardinals [A reflection theorem for i-weight , Topology Proc. 28 (2004), no. 1, 277–281]. We show that in ZFC i-weight reflects all cardinals for the class of compact LOTS. We define local i-weight, then calculate i-weight of locally compact LOTS and paracompact spaces in terms of the extent of ...