in this article we introduce the concept of $z^circ$-filter on a topological space $x$. we study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $c(x)$,  the ring of real-valued continuous functions on a completely regular hausdorff space $x$. it is observed that $x$ is a compact space if and only if every $z^circ$-filter ...

We consider C -compact orthogonally additive operators in vector lattices. After providing some examples of on a lattice with values Banach space we show that the set those is projection band Dedekind complete all regular operators. In second part article introduce new class lattices, called -complete, and any laterally-to-norm continuous operator from -complete to narrow, which generalizes res...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).