Chow, Theresa Kee Yu (1969) The Egoroff property and its relation to the order topology in the theory of Riesz spaces. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10072002-143502
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A sequence(f[subscript]n : n = 1, 2, ...) in a Riesz space L is order convergent to an element [...] whenever there exists a sequence [...] in L such that [...] holds for all n. Sequential order convergence defines the order topology on L. The closure of a subset S in this topology is denoted by cl(S). The pseudo order closure S' of a subset S is the set of all [...] such that there exists a sequence in S which is order convergent to f. If S' = cl(S) for every convex subset S, then S' = cl(S) for every subset S. L has the Egoroff property if and only if S' = cl(S) for every order bounded subset S of L. A necessary and sufficient condition for L to have the property that S' = cl(S) for every subset S of L is that L has the strong Egoroff property. A sequence(f[subscript]n : n = 1, 2, ...) in a Riesz space L is ru-convergent to an element [...] whenever there exists a real sequence [...] and an element [...] such that [...] holds for all n. Sequential ru-convergence defines the ru-topology on L. The closure of a subset S in this topology is denoted by [...]. The pseudo ru-closure S'[subscript ru] of a subset S is the set of all [...] such that there exists a sequence in S which is ru-convergent to f. If L is Archimedean, then [...] for every convex subset S implies that [...] for every subset S. A characterization of those Archimedean Riesz spaces L with the property that [...] for every subset S of L is obtained. If [...] is a monotone seminorm on a Riesz space L, then a necessary and sufficient condition for [...] in L implies [...] is that the set [...] is order closed. For every monotone seminorm [...] on L, the largest [...]-Fatou monotone serninorm bounded by [...] is the Minkowski functional of the order closure of [...]. A monotone seminorm p on a Riesz space L is called strong Fatou whenever [...]. A characterization of those Riesz spaces L which have the following property is given: "For every monotone seminorm [...], the largest strong Fatou monotone seminorm bounded by [...] : [...]." A similar characterization for Boolean algebras is also obtained.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||7 April 1969|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||07 Oct 2002|
|Last Modified:||26 Dec 2012 03:04|
- Final Version
See Usage Policy.
Repository Staff Only: item control page