The F- Topology on Space of Zero Dimensional rings

Let R be a subring of a ring T, and let F be a non-principal ultrafilter on the natural numbers IN. We consider properties and applications of a countably compact, Hausdorff topology called the "F-topology" defined on space of all zero-dimensional subring of T that contains a fixed subring R. We show that the F-topology is strictly finer than the Zariski topology. We extend results regarding distinguished spectral topologies on the space of zero-dimensional subring.

Some Results in Neutrosophic Soft Topology Concerning Neutrosophic Soft ∗ b Open Sets

In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗ b open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗ b open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets. Then, with the application of this new definition, some soft neutrosophical separation axioms, countability theorems, and countable space can be Hausdorff space under the subjection of neutrosophic soft sequence which is convergent, the cardinality of neutrosophic soft countable space, engagement of neutrosophic soft countable and uncountable spaces, neutrosophic soft topological features of the various spaces, soft neutrosophical continuity, the product of different soft neutrosophical spaces, and neutrosophic soft countably compact that has the characteristics of Bolzano Weierstrass Property (BVP) are studied. In addition to this, BVP shifting from one space to another through neutrosophic soft continuous functions, neutrosophic soft sequence convergence, and its marriage with neutrosophic soft compact space, sequentially compactness are addressed.

On Certain Covering Properties and Minimal Sets of Bigeneralized Topological Spaces

We introduce q-Lindelöf, u-Lindelöf, p-Lindelöf, s-Lindelöf, q-countably-compact, u-countably-compact, p-countably-compact, and s-countably-compact as new covering concepts in bigeneralized topological spaces via q-open sets and u-open sets in bigeneralized topological spaces. Relationships between them are studied. As two symmetries relationships, we show that q-Lindelöf and u-Lindelöf are equivalent concepts, and that q-countably-compact and u-countably-compact are equivalent concepts. We focus on continuity images of these covering properties. Finally, we define and investigate minimal q-open set, minimal u-open set, and minimal s-open sets as three new types of minimality in bigeneralized topological spaces.