Base-normality and product spaces

σ-Normality of Topological Spaces

σ-normality of topological spaces

$C^{*}$-semi-inner product spaces

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

Paracompactness and Product Spaces

A topological space is called paracompact (see [2 J) if (i) it is a Hausdorff space (satisfying the T2 axiom of [l]), and (ii) every open covering of it can be refined by one which is "locally finite" ( = neighbourhood-finite; that is, every point of the space has a neighbourhood meeting only a finite number of sets of the refining covering). J. Dieudonné has proved [2, Theorem 4] that every se...

Normality and non-normality of group compactifications in simple projective spaces

If G is a complex simply connected semisimple algebraic group and if λ is a dominant weight, we consider the compactification Xλ ⊂ P (