Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

This paper work new and unprecedented definitions of sets, which we have named supra fan, supra. delta fan, supra. semi delta fan sets, which are generated by three sets of specific type of supra open sets, it was utilized supra open, supra delta open, supra. semi delta open sets with special conditions. It is highlighted many details of these new types of fan sets, their axis, blades and their annular sets using tables. Attention is given to the interior and the closure of these three types in supra topological spaces. The research was further enriched numerous and diverse examples. Subsequently, the focus shifted to supra. semi delta fan sets to prove lemma and theorem.

The research aims to know the availability of supra-cognitive thinking skills in the questions and activities of the computer book for the fifth grade preparatory scientific and literary branches in Iraq for the academic year 2018/2019, as the researcher has prepared a list of supra-cognitive thinking skills included two areas and (6) key skills and (27) A sub - skill, where by the questions and activities of the aforementioned authors were analyzed. The researcher followed the descriptive analytical approach "method of content analysis", and adopted the explicit and implicit unit of analysis, as was verified the validity and stability of the analysis, and the results showed unevenness and imbalance in the distribution of supra-cognitive th

In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2)   are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory. 

The significance fore supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extension to supra open sets, including supra semi open sets, supra per open and others. In this research, a notion for ⱨ-supra open created within the generalizations of the supra topology of sets. Our investigation involves harnessing this style of sets to introduce modern notions in these spaces, specifically supra ⱨ - interior, supra ⱨ - closure, supra ⱨ - limit points, supra ⱨ - boundary points and supra ⱨ - exterior of sets. It has been examining the relationship with supra open. The research was also enriched with many

We examine 10 hypothetical patients suffering from some of the symptoms of COVID 19 (modified) using topological concepts on topological spaces created from equality and similarity interactions and our information system. This is determined by the degree of accuracy obtained by weighing the value of the lower and upper figures. In practice, this approach has become clearer.

    Soft clays are generally characterized by low shear strength, low permeability and high compressibility. An effective method to accelerate consolidation of such soils is to use vertical drains along with vacuum preloading to encourage radial flow of water.  In this research numerical modeling of prefabricated vertical drains with vacuum pressure was done to investigate the effect of using vertical drains together with vacuum pressure on the degree of saturation of fully and saturated-unsaturated soft soils.  Laboratory experiments were conducted by using a specially-designed large consolidometer cell where a central drain was installed and vacuum pressure was applied. All tests were conducted

We define and study new ideas of fibrewise topological space on D namely fibrewise multi-topological space on D. We also submit the relevance of fibrewise closed and open topological space on D. Also fibrewise multi-locally sliceable and fibrewise multi-locally section able multi-topological space on D. Furthermore, we propose and prove a number of statements about these ideas.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise near compact and fibrewise locally near compact spaces, which are generalizations of well-known concepts near compact and locally near compact topological spaces. Moreover, we study relationships between fibrewise near compact (resp., fibrewise locally near compact) spaces and some fibrewise near separation axioms.

F index is a connected graph, sum of the cubes of the vertex degrees. The forgotten topological index has been designed to be employed in the examination of drug molecular structures, which is extremely useful for pharmaceutical and medical experts in understanding the biological activities. Among all the topological indices, the forgotten index is based on degree connectivity on bonds. This paper characterized the forgotten index of union of graphs, join graphs, limits on trees and its complements, and accuracy is measured. Co-index values are analyzed for the various molecular structure of chemical compounds