منابع مشابه
Quotients of Proximity Spaces
A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...
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A Bing space is a compact Hausdorff space whose every component is a hereditarily indecomposable continuum. We investigate spaces which are quotients of a Bing space by means of a map which is injective on components. We show that the class of such spaces does not include every compact space, but does properly include the class of compact metric spaces. Our entire development is based on Krasin...
متن کاملQuotients of F-spaces
Let X be a non-locally convex F-space (complete metric linear space) whose dual X' separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space XIN does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a...
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The notion of smooth biproximity space where $delta_1,delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,delta_1,delta_2)$ induces a supra smooth proximity space $delta_{12}$ finer than $delta_1$ and $delta_2$. We study the relationship between $(X,delta_{12})$ and the $FP^*$-separation axioms which had been introduced by...
متن کاملQUOTIENTS OF BANACH SPACES OF COTYPE q
Let Z be a Banach space and let X c Z be a ¿-convex subspace (equivalently, assume that X does not contain /¡"s uniformly). Then every Bernoulli series 2¡?_! e„z„ which converges almost surely in the quotient Z/X can be lifted to a Bernoulli series a.s. convergent in Z. As a corollary, if Z is of cotype q, then Z/X is also of cotype q. This extends a result of [4] concerning the particular case...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.2307/2039491