Strongly base-paracompact spaces
نویسندگان
چکیده
A space X is said to be strongly base-paracompact if there is a basis B for X with |B| = w(X) such that every open cover of X has a star-finite open refinement by members of B. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions F with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from F .
منابع مشابه
On the Para - Compactness of Cone Metric Spaces 1
In 2007, Long-Guang and Xian[3] replaced introduced cone metric spaces. They replaced the set of real numbers by an ordered Banach space in the definition of metric and generalized the notion of metric space. Recently, Ayse Sönemaz [5] proved a cone metric space with a normal cone, of course it has to be strongly minihedral, is paracompact. In this paper we omit the strongly minihedral of cone....
متن کاملContinuous Separating Families in Ordered Spaces and Strong Base Conditions
In this paper we study the role of Stepanova’s continuous separating families in the class of linearly ordered and generalized ordered spaces and we construct examples of paracompact spaces that have strong base properties (such as point-countable bases or σ-disjoint bases), have continuous separating families, and yet are non-metrizable. MR Classification Numbers: Primary 54F05, 54E35; Seconda...
متن کاملB Paracompact Does Not Imply B1 Paracompact1
As is well known the category of paracompact spaces is important in algebraic topology and the theory of fiber spaces. The following question arises naturally. If a space (Hausdorff space) B is paracompact, is the space of paths B1 (I = [0, l]), with, of course, the compact-open topology, also paracompact? The following simple example answers the question in the negative. Let X denote the set o...
متن کاملParacompactness on supra topological spaces
In this article, we present the concept of supra paracompact spaces and study its basic properties. We elucidate its relationship with supra compact spaces and prove that the property of being a supra paracompact space is weakly hereditary and topological properties. Also, we provide some examples to show some results concerning paracompactness on topology are invalid on supra topology. Finally...
متن کاملNormal spaces and fixed points of &h-Stone extensions
We present two examples of nice normal spaces X having the property that for some fixedpoint free homeomorphism on X its tech-Stone extension has a fixed point. One of the spaces presented here is locally countable, locally compact, separable, normal, countably paracompact and weakly zero-dimensional. The other one is hereditarily normal and strongly zero-dimensional. Our construction of this e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010