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- KCI
ISSN : 1226-0657
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Vol.6 No.1
Abstract
Let <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>).
Abstract
The purpose of this paper is to show that by the divisibility of a direct injective module, we obtain some results with respect to a direct injective module.
Abstract
We introduce the notion of the <TEX>$\omega$</TEX>-derived set and <TEX>$\omega$</TEX>-dense, and investigate some of their properties.
Abstract
In this paper, we investigate the properties of the Dunford-Schwartz integral (the integral with respect to a finitely additive measure). Though it is not equivalent to the cylinder integral, we can show that a cylinder probability v on (H, C) can be extend as a finitely additive probability measure <TEX>$\hat{v}$</TEX> on a field <TEX>$\hat{C}{\;}{\supset}{\;}C$</TEX> which is equivalent to the Dunford-Schwartz integral on (<TEX>$H,{\;}\hat{C},{\;}\hat{v}$</TEX>).
Abstract
In this paper, we show that the existence of the solutions to the variational-type inequalities for set-valued mappings on normed linear spaces using Fan's section theorem.
Abstract
We obtain a generalization of Behera and Panda's result on nonlinear scalar case to the vector version.
Abstract
The concept of pseudoLindelof spaces is introduced. It is shown that the followings are equivalent: (a) for any two disjoint zero-sets in X, at least one of them is Lindelof, (b) <TEX><TEX>$\mid$</TEX>vX{\;}-{\;}X<TEX>$\mid$</TEX>{\leq}{\;}1$</TEX>, and (c) for any space T with <TEX>$X{\;}{\subseteq}{\;}T$</TEX>, there is an embedding <TEX>$f{\;}:{\;}vX{\;}{\rightarrow}{\;}vT$</TEX> such that f(x) = x for all <TEX>$x{\;}{\in}{\;}X$</TEX> and that if <TEX>$X{\;}{\times}{\;}Y$</TEX> is a z-embedded pseudoLindelof subspace of <TEX>$vX{\;}{\times}{\;}vY,{\;}then{\;}v(X{\;}{\times}{\;}Y){\;}={\;}vX{\;}{\times}{\;}vY$</TEX>.
Abstract
In this note we give a characterization on weak convergence of bounded linear functionals in <TEX>$\sigma$</TEX>-complete abstract M spaces.