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...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

We investigate properties of the class of compact spaces on which every regular Borel measure is separable. This class will be referred to as MS. We discuss some closure properties of MS, and show that some simply deened compact spaces, such as compact ordered spaces or compact scattered spaces, are in MS. Most of the basic theory for regular measures is true just in ZFC. On the other hand, the...

In this paper, we establish the relationships between spaces with a compact-countable weak-base and spaces with various compact-countable networks, and give two mapping theorems on spaces with compact-countable weakbases. Weak-bases and g-first countable spaces were introduced by A.V.Arhangel’skii [1]. Spaces with a point-countable weak-base were discussed in [5,6], and spaces with a locally co...

The main purpose of this paper is to establish general conditions under which T2-spaces are compact-covering images of metric spaces by using the concept of cfpcovers. We generalize a series of results on compact-covering open images and sequencecovering quotient images of metric spaces, and correct some mapping characterizations of g-metrizable spaces by compact-covering σ-maps and mssc-maps.