Volume 61 , issue 3 ( 2009 ) | back |
A new hyperspace topology and the study of the function space θ∗-LC(X,Y) | 181--193 |
Abstract
The intent of this paper is to introduce a new hyperspace topology on the collection of all θ-closed subsets of a topological space. The space of all θ∗-lower semicontinuous functions has been studied in detail and finally we deal with some multifunctions.
Keywords: θ-closed set; H-closed space; H-set; θ-partially ordered space; θ∗-lower semicontinuous functions; multifunctions.
MSC: 54B20, 54C35
Selection principles and Baire spaces | 195--202 |
Abstract
We prove that if X is a separable metric space with the Hurewicz covering property, then the Banach-Mazur game played on X is determined. The implication is not true when ``Hurewicz covering property" is replaced with ``Menger covering property".
Keywords: Baire space; First category; Banach-Mazur game; Menger property; Hurewicz property.
MSC: 03E99, 54D20, 54E52
Some results in fixed point theory concerning generalized metric spaces | 203--208 |
Abstract
In this paper we shall study the fixed point theory in generalized metric spaces (gms). One of our results will be a generalization of Kannan's fixed point theorem in the ordinary metric spaces, and Das's fixed point theorem in gms.
Keywords: Generalized metric space; Fixed point.
MSC: 54H25, 47H10
On so-metrizable spaces | 209--218 |
Abstract
In this paper, we give some new characterizations for so-metrizable spaces, which answers a question posed by Z. Li and generalize some results on so-metrizable spaces. As some applications of the above results, some mappings theorems on so-metrizable spaces are obtained.
Keywords: so-network,; sof-countable; so-metrizable space.
MSC: 54C10, 54D50, 54E35, 54E99
On L1-convergence of certain generalized modified trigonometric sums | 219--226 |
Abstract
In this paper we define new modified generalized sine sums Knr(x)=12sinx∑nk=1(△rak−1−△rak+1)˜Sr−1k(x) and study their L1-convergence under a newly defined class \boldKα. Our results generalize the corresponding results of Kaur, Bhatia and Ram [6] and Kaur~[7].
Keywords: L1−convergence; conjugate Cesàro means; generalized sine sums.
MSC: 42A20, 42A32
Compactness and weak compactness of elementary operators on B(l2) induced by composition operators on l2 | 227--233 |
Abstract
In this paper we have given simple proofs of some range inclusion results of elementary operators on B(l2) induced by composition operators on l2. By using these results we have characterized compact and weakly compact elementary operators on B(l2) induced by composition operators on l2.
Keywords: Compactness; composition operators; elementary operators; thin operators.
MSC: 47B33, 47B47
Riesz spaces of measures on semirings | 235--239 |
Abstract
It is shown that the spaces of finite valued signed measures (signed charges) on σ-semirings (semirings) are Dedekind complete Riesz spaces, which generalizes known results on σ-algebra and algebra cases.
Keywords: Riesz spaces; semiring; measure
MSC: 28C99, 46G12
Characterizations of δ-stratifiable spaces | 241--246 |
Abstract
In this paper, we give some characterizations of
δ-stratifiable spaces by means of g-functions and semi-continuous
functions. It is established that:
\item{(1)} A topological space X in which every point is a regular
Gδ-set is δ-stratifiable if and only if there
exists a g-function g:N×X→τ satisfies
that if F∈RG(X) and y∉F, then there is an m∈N
such that y∉¯g(m,F);
\item{(2)} If there is an order preserving map φ:USC(X)→LSC(X) such
that for any h∈USC(X),0≤φ(h)≤h and
$0<\varphi(h)(x)
Keywords: δ-stratifiable spaces; g-functions; upper semi-continuous maps; lower semi-continuous maps.
MSC: 54E20, 54C08; 26A15