scholarly journals Regular vector lattices of continuous functions and Korovkin-type theorems–-Part II

2006 ◽  
Vol 172 (1) ◽  
pp. 69-90 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano
Keyword(s):  
Continuous Functions ◽  
Vector Lattices ◽  
Korovkin Type Theorems

scholarly journals Regular vector lattices of continuous functions and Korovkin-type theorems–-Part I

2005 ◽  
Vol 171 (3) ◽  
pp. 239-260 ◽  
Author(s):  
Francesco Altomare ◽  
Mirella Cappelletti Montano
Keyword(s):  
Continuous Functions ◽  
Vector Lattices ◽  
Korovkin Type Theorems

Free Vector Lattices

1968 ◽  
Vol 20 ◽  
pp. 58-66 ◽  
Author(s):  
Kirby A. Baker
Keyword(s):  
Universal Algebra ◽  
Vector Lattice ◽  
Piecewise Linear ◽  
Continuous Functions ◽  
Real Numbers ◽  
Vector Lattices ◽  
Explicit Characterization

This note presents a useful explicit characterization of the free vector lattice FVL(ℵ) on ℵ generators as a vector lattice of piecewise linear, continuous functions on Rℵ, where ℵ is any cardinal and R is the set of real numbers. A transfinite construction of FVL(ℵ) has been given by Weinberg (14) and simplified by Holland (13, § 5). Weinberg's construction yields the fact that FVL(ℵ) is semi-simple; the present characterization is obtained by combining this fact with a theorem from universal algebra due to Garrett Birkhoff.

Order-Cauchy Completions of Rings and Vector Lattices of Continuous Functions

1980 ◽  
Vol 32 (3) ◽  
pp. 657-685 ◽  
Author(s):  
F. Dashiell ◽  
A. Hager ◽  
M. Henriksen
Keyword(s):  
Continuous Functions ◽  
Topological Properties ◽  
Order Convergence ◽  
Sequential Order ◽  
Compact Spaces ◽  
Lattice Group ◽  
Vector Lattices ◽  
Topological Condition ◽  
Bounded Continuous Functions ◽  
Tychonoff Spaces

This paper studies sequential order convergence and the associated completion in vector lattices of continuous functions. Such a completion for lattices C(X) is related to certain topological properties of the space X and to ring properties of C(X). The appropriate topological condition on the space X equivalent to this type of completeness for the lattice C(X) was first identified, for compact spaces X, in [6]. This condition is that every dense cozero set S in X should be C*-embedded in X (that is, all bounded continuous functions on S extend to X). We call Tychonoff spaces X with this property quasi-F spaces (since they generalize the F-spaces of [12]).In Section 1, the notion of a completion with respect to sequential order convergence is first described in the setting of a commutative lattice group G.

scholarly journals Some Applications of New Modifiedq-Integral Type Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
R. P. Pathak ◽  
Shiv Kumar Sahoo
Keyword(s):  
Approximation Theorem ◽  
Integral Operators ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Unit Interval ◽  
Polynomial Space ◽  
Integral Type ◽  
Space Of Continuous Functions ◽  
Approximation Process ◽  
Korovkin Type Theorems

We introduce a new sequence ofq-integral operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on unit interval. Weighted statistical approximation theorem, Korovkin type theorems for fuzzy continuous functions, and an estimate for the rate of convergence for these operators.

scholarly journals The order topology for function lattices and realcompactness

1981 ◽  
Vol 4 (2) ◽  
pp. 289-304 ◽  
Author(s):  
W. A. Feldman ◽  
J. F. Porter
Keyword(s):  
Uniform Convergence ◽  
Continuous Functions ◽  
Order Topology ◽  
Convergence Space ◽  
Vector Lattices ◽  
Convergence Structure ◽  
Relative Uniform Convergence ◽  
Compact Convergence

A latticeK(X,Y)of continuous functions on spaceXis associated to each compactificationYofX. It is shown forK(X,Y)that the order topology is the topology of compact convergence onXif and only ifXis realcompact inY. This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes everyC(X)and all countably universally complete function lattices with 1. It is shown that a choice ofK(X,Y)endowed with a natural convergence structure serves as the convergence space completion ofVwith the relative uniform convergence.

scholarly journals On vector lattices and rings of uniformly continuous functions

1966 ◽  
Vol 6 (1) ◽  
pp. 23-29
Author(s):  
L. Aparina
Keyword(s):  
Continuous Functions ◽  
Vector Lattices ◽  
Uniformly Continuous

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Л. В. Апарина. О векторных решетках и кольцах равномерно непрерывных функций L. Aparina. Apie tolygiai tolydinių funkcijų vektorines gardeles ir žiedus

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