The Ray space of a right process

Ronald K. Getoor; Michael J. Sharpe

Displaying similar documents to “The Ray space of a right process”

On the Ray topology

Frank B. Knight (1984)

Séminaire de probabilités de Strasbourg

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Function space topologies deriving from hypertopologies and networks

A. Di Concilio, A. Miranda (2001)

Bollettino dell'Unione Matematica Italiana

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In un progetto di generalizzazione delle classiche topologie di tipo «set-open» di Arens-Dugundji introduciamo un metodo generale per produrre topologie in spazi di funzioni mediante l'uso di ipertopologie. Siano $X$ , $Y$ spazi topologici e $C (X, Y)$ l'insieme delle funzioni continue da $X$ verso $Y$ . Fissato un «network» $α$ nel dominio $X$ ed una topologia $τ$ nell'iperspazio $C L (Y)$ del codominio $Y$ si genera una topologia $τ_{α}$ in $C (X, Y)$ richiedendo che una rete $\{f_{λ}\}$ di $C (X, Y)$ converge in $τ_{α}$ ad $f \in C (X, Y)$ se e solo se la rete $\{\bar{f_{λ} (A)}\}$ converge...

Strong topologies on vector-valued function spaces

Marian Nowak (2000)

Czechoslovak Mathematical Journal

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Let $(X, ∥ \cdot ∥_{X})$ be a real Banach space and let $E$ be an ideal of $L^{0}$ over a $σ$ -finite measure space $(Ø, Σ, μ)$ . Let $(X)$ be the space of all strongly $Σ$ -measurable functions $f Ø \to X$ such that the scalar function $\tilde{f}$ , defined by $\tilde{f} (ø) = {∥ f (ø) ∥}_{X}$ for $ø \in Ø$ , belongs to $E$ . The paper deals with strong topologies on $E (X)$ . In particular, the strong topology $β (E (X), E {(X)}_{n}^{\sim})$ ( $E {(X)}_{n}^{\sim} =$ the order continuous dual of $E (X)$ ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.

Pointwise convergence and the Wadge hierarchy

Alessandro Andretta, Alberto Marcone (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show that if $X$ is a $Σ_{1}^{1}$ separable metrizable space which is not $σ$ -compact then $C_{p}^{*} (X)$ , the space of bounded real-valued continuous functions on $X$ with the topology of pointwise convergence, is Borel- $Π_{1}^{1}$ -complete. Assuming projective determinacy we show that if $X$ is projective not $σ$ -compact and $n$ is least such that $X$ is $Σ_{n}^{1}$ then $C_{p} (X)$ , the space of real-valued continuous functions on $X$ with the topology of pointwise convergence, is Borel- $Π_{n}^{1}$ -complete. We also prove a simultaneous improvement of theorems...

Fine connectedness and alpha-excessive functions

S. Ramaswamy (1972)

Annales de l'institut Fourier

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In this article, for any Standard Process $X$ and for any $α \geq 0$ , the conditions under which an $α$ -excessive function, vanishing at a point, vanishes identically are investigated.

The quasi Isbell topology on function spaces

D. N. Georgiou, A. C. Megaritis (2015)

Colloquium Mathematicae

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In this paper, on the family (Y) of all open subsets of a space Y we define the so called quasi Scott topology, denoted by $τ_{q S c}$ . This topology defines in a standard way, on the set C(Y,Z) of all continuous maps of the space Y to a space Z, a topology $t_{q I s}$ called the quasi Isbell topology. The latter topology is always larger than or equal to the Isbell topology, and smaller than or equal to the strong Isbell topology. Results and problems concerning the topology $t_{q I s}$ are given.