We point out that in metric spaces Haver’s property is not equivalent to the property introduced by Addis and Gresham. We prove that they are equal when the space has the Hurewicz property. We prove several results about the preservation of Haver’s property in products. We show that if a separable metric space has the Haver property, and the nth power has the Hurewicz property, then the nth pow...

We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(ω) with the Cantor set topology.

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. In Patterson and Savas (2006) extended the definitions presented in (Patterson, 2003) to l...

This paper presents some common fixed point theorems for weakly compatible mappings via an implicit relation in Fuzzy Menger spaces satisfying the common property (E.A)

We explore the connections between selection games on Hausdorff spaces and their corresponding Vietoris space of compact subsets. These considerations offer a similar relationship as well-known ?-covers X ordinary open covers finite powers X. The primary utility this method is to establish relationships with k-covers Particularly, we show that some commonly studied principles are equivalent rel...

This corrigendum provides a correction to the paper entitled “β−Menger and β−Hurewicz spaces”.

We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babink...