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Vol.5 No.1
Abstract
Let f : X longrightarrow Y be quasi-open. We show that: (1) If A <TEX>$\subset$</TEX> X is open, f│A is quasi-open, (2) f : X longrightarrow f(X) is quasi-open. (3) And let <TEX>$f_{\alpha}/,:X_{\alpha}$</TEX>, longrightarrow <TEX>$Y_{\alpha}$</TEX> be quasi-open. Then <TEX>$\Pi f_{\alpha}, : \Pi X_{\alpha}$</TEX> longrightarrow <TEX>$\Pi Y_{\alpha}$</TEX>/ defined by {<TEX>$x_{\alpha}$</TEX>} longrightarrow {<TEX>$f_{\alpha},({\chi}_{\alpha}$</TEX>)}, is quasi-open. (4) Lastly, if <TEX>$f_{i}: X_{i}$</TEX> longrightarrow Y are quasi-open, i = 1,2, then F: <TEX>$X_1 \bigoplus X_2$</TEX> longrightarrow Y, defined by <TEX>$F({\chi})=f_i({\chi})$</TEX>, <TEX>${\chi} \in X_i$</TEX>, is also quasi-open.
Abstract
We evaluate the sum of certain class of generalized hypergeometric series of unit argument. Summation formulas, contiguous to Watson's, Whipple's, Lavoie's and Choi's theorems in the theory of the generalized hypergeometric series, are obtained. Certain limiting cases of these results are given.
Abstract
For continuous maps f of the circle to itself, we show that (1) every <TEX>$\omega$</TEX>-limit point is recurrent (or almost periodic) if and only if every <TEX>$\omega$</TEX>-limit set is minimal, (2) every <TEX>$\omega$</TEX>-limit set is almost periodic, then every <TEX>$\omega$</TEX>-limit set contains only one minimal set.
Abstract
In [5], Zhu introduces a bounded operator T from <TEX>$L^{\infty}$</TEX>(D) into Bloch space B. In this paper, we will consider the generalized Bloch spaces <TEX>$B_{q}$</TEX> and find bounded operator from <TEX>$L^{\infty}$</TEX>(D) into <TEX>$B_{q}$</TEX>.
Abstract
In the present paper the author studies the decomposition property (<TEX>$\delta$</TEX>) of the bounded linear operators.
Abstract
This paper is concerned with the existence of mutiple positive solution of (equation omitted) with Dirichlet boundary condition.
Abstract
We study the space-times that have a unique terminal indecomposable past set or a unique terminal indecomposable future set and examine their causal boundary, and we investigate some conditions for the warped product space-times of the form (a, b) <TEX>${\times}_fF$</TEX> to have a unique terminal indecomposable past set or a unique terminal indecomposable future set.
Abstract
A Gauss map of m-dimensional distribution on a Riemannian manifold M is called a harmonic Gauss map if it is a harmonic map from the manifold into its Grassmann bundle <TEX>$G_m$</TEX>(TM) of m-dimensional tangent subspace. We calculate the tension field of the Gauss map of m-dimensional distribution and especially show that the Hopf fibrations on <TEX>$S^{4n＋3}$</TEX> are the harmonic Gauss map of 3-dimensional distribution.
Abstract
We investigate a chain of properties of real function algebras along the analogous proofs of the complex cases such as the fact that any real function algebra which is both maximal and essential is pervasive. And some properties of real function algebras with a vertex property will be discussed.
Abstract
Let <TEX>$H_1$</TEX> (<TEX>$\Delta$</TEX>, M) be the family of all 1-1 holomorphic mappings of the unit disk <TEX>$\Delta\; \subset\; C$</TEX> into a complex manifold M. Following the method of Royden, Hahn introduces a new pseudo-differential metric <TEX>$S_{M}$</TEX> on M. The present paper is to study the product property of the metric <TEX>$S_{M}$</TEX> when M is given by the product of two domains <TEX>$D_1$</TEX> and <TEX>$D_2$</TEX> in the complex plane C, thus investigating the hyperbolicity of the product domain <TEX>$D_1 \;\times\; D_2$</TEX> with respect to <TEX>$S_{M}$</TEX> metric.
Abstract
In this paper, we study an (n ＋ 1)-dimensional compact, orientable, minimal contact CR-submanifold of (n - 1) ontact CR-dimension in a (2m ＋ 1)-dimensional unit sphere <TEX>$S^{2m＋1}$</TEX> in terms of integral formula.