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...

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...

Every open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed sets F0, F1 ⊂ X , with f(F0) = Y = f(F1), provided all fibers of f are infinite and C∗-embedded in X . Applications are demonstrated for the existence of “disjoint” usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and for special type of factorizations of open co...

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 l...

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....

1. Stone2 has proved that a space is fully normal 7\ if and only if it is paracompact T2. If throughout his proof T\ is deleted and T2 is replaced by T4 (normality), we obtain that a space is fully normal if and only if it is paracompact TV In this note we prove that 7*2 can also be replaced by any one of the following: T2. Every two points with disjoint closures have disjoint neighborhoods. Ti...

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...

In 1951, Dowker proved that a space X is countably paracompact and normal if and only if X×I is normal. A normal space X is called a Dowker space if X × I is not normal. The main thrust of this article is to extend this work with regards α-normality and β-normality. Characterizations are given for when the product of a space X and (ω + 1) is α-normal or β-normal. A new definition, α-countably p...