In this study, we first introduce a new class of spaces, namely soft expandable which is generalization paracompact and countably compact spaces. Some properties these spaces that are discussed in paper the space equivalent to every A?-soft cover has softLF open refinement. Also, discuss under what conditions paracompact. With help interesting examples, elucidate there no relationship between topology its parametric topologies with respect possession property being space. regards, role...

It is well known that certain topological concepts such as the sum of topologies and product are defined by particular classes other topologies. In others, it crucial to look into connections between these topology generated them. One creates a family general soft topology, which over sets satisfying basic axioms topology. interesting investigate how notions behave when applied because enables us study qualities comparing them their counterparts in this paper, we benefit from fruitful...

<abstract> Herein, we applied soft somewhere dense sets to initiate six sorts of spaces called almost (nearly, mildly) $ SD $-compact and $-Lindelöf spaces. We study the master properties these illustrate relations between them with help examples. In addition, clarify that are equivalent under a $-partition. Moreover, relationships initiated enriched topological other well-known such as S $-connected indicated. </abstract>

In this work, we use the notion of $g \mu$-paracompact space \cite{ADeb} to introduce two types sets called $\alpha$-$g and $\beta$-$g \mu$-paracompact. We show that every set is if a generalized topological $(S,\mu)$ \mu$-paracompact, then $\mu$-closed subset in while $\mu g$-closed $(S, \mu)$ Finally, $co$-$\alpha$-$g\mu$-paracompact as an application $\alpha$-$g\mu$-paracompact study some its features.

&lt;abstract&gt;&lt;p&gt;A new generalization of classical topology, namely infra topology was introduced. The importance studying this structure comes from two matters, first preserving topological properties under a weaker condition than and second, the possibility applying infra-interior infra-closure operators to study rough-set concepts. Herein, we familiarize concepts in establish their master properties. First, introduce notions infra-connected locally spaces. Among some results...

A hereditary class on a set $X$ is nonempty collection of subsets closed under the property. In this paper, we define and study notion Lindelöfness in generalized topological spaces with respect to called, $\mu\mathcal{H}$-Lindelöf discuss their properties.

The aim of this paper is to introduce and study the class $g\omega \beta$-closed sets. This sets finer than $g$-closed $\omega \beta- $closed We fundamental properties Further, we \beta$-open sets, \beta$-neighborhoodsets, \beta$-continuous functions, \beta$-irresolute functions functions.

In this paper, we use the soft set theory and concept of semi-linear uniform spaces to introduce notion with its generalization, briefly soft-GSLUS. We investigate some properties topology that induced by Also, members soft-GSLUS define a proximity space filter then establish relationships between them. Finally, give perceptual application structures employing natural transformation proximity.

The aim of this paper is to introduce and study some types m-compactness with respect a hereditary class called weakly mH-compact spaces subsets. We will provide several characterizations investigate their relationships other classes generalized topological spaces.

In this paper, we present a new generalization for somewhere dense of topological space (Z, τ ), namely ωSWD-open subsets. We introduce the concept family and discuss some their properties with help illustrative example. Moreover, will show if ) is anti-locally countable finer than cocountable topology then class subsets be equivalent. more most important which theorem in [1]. Furthermore, finish work by shedding light on one type covering where study notion almost ωSWD-compact spaces properties.

Soft set theory is a topic of interest for many researches working in various fields. In order to advance this field study, we invest the soft pre-open sets introduce new generalization soft-expandable, namely so(pre)ft-expandable. We used locations definition soft-expandable spaces give either equivalent definitions expandable or different types spaces, will show connections between them and based on these connections, definition(pre) space was chosen. Relationships topological with other...

In [18], Tallafha and Khalil introduced a new type of uniform space which is mixture topology analysis, namely semi-linear spaces. this paper, we continue extend study by presenting generalization space, weak Then present the concept proximinal sets without any tools that metric structure usually offers. We show every finite set convergent sequence with its limit are sets. Furthermore, give characterization metrizable spaces some topological properties

In this paper we introduce a new class of generalizations continuous functions via ωβ-open sets called weakly ωβ-continuous functions. Moreover, study some its fundamental properties and characterizations. The concept weak is weaker than ωβ-continuous, ω-continuous β-continuous functions, are also discussed.

We introduce the class of β 1 -paracompact spaces in topological and give characterizations such spaces.We study subsets subspaces discuss their properties.Also, we investigate invariants by functions.

In [1], Aljarrah and Noorani introduced a new class of generalizations continuous functions via ωβ – open sets called weakly functions, they gave some its fundamental properties characterizations. this paper we continue the investigation more characterization. Also relationships between compact spaces are introduced.

In this paper we generalize the notion of \(\omega \beta\)-open sets in setting bitopological spaces and study their fundamental properties. Also utilize them to define pairwise \beta\)-\({T_i}\) for \(i = 0,1,2\) \beta\)-\({R_j}\) \(j 0,1\).

The aim of this paper is to introduce and study strong forms $\mu$-Lindelöfness in generalized topological spaces with a hereditary class, called $\mathcal{S} \mu\mathcal{H}$-Lindelöfness $\mathbf{S}-\mathcal{S}\mu\mathcal{H}$-Lindelöfness. Interesting characterizations these are presented. Several effects various types functions on them studied.

A new class of sets called generalized δω−closed in topological spaces is introduced and some their basic properties are investigated. This lies between the closed (X, τ ). Moreover, we provide several relatively decompositions continuity. Several examples provided to illustrate behavior sets.

Abstract In this paper we introduce and study a new class of sets, namely γ−countably paracompact sets. We characterize sets some its basic properties. obtain that is weaker than α−countably stronger β−countably