Processing math: 100%
Volume 61 , issue 3 ( 2009 )back
A new hyperspace topology and the study of the function space θ-LC(X,Y)181--193
S. Ganguly, Sandip Jana and Ritu Sen

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.

Creative Commons License

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 spaces195--202
Marion Scheepers

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".

Creative Commons License

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 spaces203--208
Ali Fora, Azzeddine Bellour and Adnan Al-Bsoul

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.

Creative Commons License

Keywords: Generalized metric space; Fixed point.

MSC: 54H25, 47H10

On so-metrizable spaces209--218
Xun Ge

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.

Creative Commons License

Keywords: so-network,; sof-countable; so-metrizable space.

MSC: 54C10, 54D50, 54E35, 54E99

On L1-convergence of certain generalized modified trigonometric sums219--226
Karanvir Singh and Kulwinder Kaur

Abstract

In this paper we define new modified generalized sine sums Knr(x)=12sinxnk=1(rak1rak+1)˜Sr1k(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].

Creative Commons License

Keywords: L1convergence; conjugate Cesàro means; generalized sine sums.

MSC: 42A20, 42A32

Compactness and weak compactness of elementary operators on B(l2) induced by composition operators on l2227--233
Gyan Prakash Tripathi

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.

Creative Commons License

Keywords: Compactness; composition operators; elementary operators; thin operators.

MSC: 47B33, 47B47

Riesz spaces of measures on semirings235--239
Z. Ercan

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.

Creative Commons License

Keywords: Riesz spaces; semiring; measure

MSC: 28C99, 46G12

Characterizations of δ-stratifiable spaces241--246
Kedian Li

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×Xτ satisfies that if FRG(X) and yF, then there is an mN such that y¯g(m,F); \item{(2)} If there is an order preserving map φ:USC(X)LSC(X) such that for any hUSC(X),0φ(h)h and $0<\varphi(h)(x)0,thenXis\delta$-stratifiable space.

Creative Commons License

Keywords: δ-stratifiable spaces; g-functions; upper semi-continuous maps; lower semi-continuous maps.

MSC: 54E20, 54C08; 26A15