منابع مشابه
Quotients of Bing Spaces
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...
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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...
متن کاملQuotients 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...
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...
متن کاملQuotients of Finite-dimensional Quasi-normed Spaces
We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to `∞ for some k. We give two results of this nature. The first guarantees a proportional dimensional cubic quotient when the envelope is cubic; the second gives an estimate for the size of a cubic quotient in terms of a measure of nonconvexity of the quasi-norm.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2008
ISSN: 0166-8641
DOI: 10.1016/j.topol.2006.12.015