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In this paper, ωs -irresoluteness as a strong form of ωs -continuity is introduced. It is proved that ωs -irresoluteness is independent of each of continuity and irresoluteness. Also, ωs -openness which lies strictly between openness and semi-openness is defined. Sufficient conditions for the equivalence between ωs -openness and openness, and between ωs -openness and semi-openness are given. Moreover, pre-ωs -openness which is a strong form of ωs -openness and independent of each of openness and pre-semi-openness is introduced. Furthermore, slight ωs -continuity as a new class of functions which lies between slight continuity and slight semi-continuity is introduced. Several results related to slight ωs -continuity are introduced, in particular, sufficient conditions for the equivalence between slight ωs -continuity and slight continuity, and between slight ωs -continuity and slight semi-continuity are given. In addition to these, ωs -compactness as a new class of topological spaces that lies strictly between compactness and semi-compactness is introduced. It is proved that locally countable compact topological spaces are ωs -compact. Also, it is proved that anti-locally countable ωs-compact topological spaces are semi-compact. Several implications, examples, counter-examples, characterizations, and mapping theorems are introduced related to the above concepts are introduced.

In this research article, we define some categories of open sets over a generalized topological space given together with a primal collection. In addition, we clarify some of its characteristics and investigate the relationships between these concepts in the space under consideration. The topic of continuity occupies a large space in topological theory and is one of the most important topics therein. Researchers have examined it in light of many variables. We followed the same approach by studying the concept of continuity between two generalized topological spaces in light of the primal collection under the name (g,P)-continuity. We also made a decomposition of this type of function in light of these weak categories of open sets.

In this paper, we investigate and explore the properties of quasi-topological loops with respect to irresoluteness. Moreover, we construct an example of a quasi-irresolute topological inverse property-loop by using a zero-dimensional additive metrizable perfect topological inverse property-loop L∗ with relative topology τ L′ .

The goal of this research is to display a new type of Nano ∼ topological space namely Nano-N*-topological space. Many classes of open sets are defined and studied the relationship among there. We investigate, some characterization of them. Finally some of their characterization are proved.

In this paper we introduce intuitionistic semi * continuous and intuitionistic contra - semi * continuous functions via the concept of intuitionistic semi * open and intuitionistic semi * closed set respectively. Also, we investigate their properties and characterization.

In this paper, a new class of open sets called Micro Sp- Open sets in Micro topological spaces are introduced and its fundamental properties are analyzed. Also, some operations on Micro Sp-open sets are investigated.

In this paper, we introduce a new class of sets called nano semi* -open sets and discuss some of its properties in nano topological space. We also, present nano semi* -interior, nano semi* -closure and study some of its fundamental properties.

In this paper, we introduce the concept of soft semi* -continuous functions and soft semi* -irresolute functions in soft topological spaces. Also, we investigate its properties and study its relation with other soft continuous functions

Exploring the relationship between formation pressure and shale pore evolution is helpful for the enrichment and development of marine shale gas accumulation theory. The thermal evolution experiment was carried out on the Xiamaling Formation (Pr3x) lowly matured marine shale, which has a similar sedimentary environment to the Longmaxi Formation (S1l) highly matured marine shale. Comparative experiments of open and semi-closed pyrolysis and multiple pore structure characterization techniques, including CO2 and N2 physisorption, mercury intrusion porosimetry, and field emission scanning electron microscopy, were conducted. The marine shale pore evolutionary model under formation pressure is proposed by characterizing pore evolution, and hydrocarbon expulsion and retention for shales under and without formation fluid pressures. The results show that the existence of formation pressure increases the percentage of quartz and reduces the content of clay minerals. The change in formation pressure has no obvious effect on the maturity evolution of shale samples. With the increase of formation pressure, the pore morphology of shale gradually changes from narrow slit pores to ink bottle-shaped pores. The retained hydrocarbons in shale mainly occupy the mesopore space, and the existence of formation pressure promotes hydrocarbon expulsion, especially the hydrocarbon expulsion in the mesopore. In addition, formation pressure improves pore connectivity, especially in the high-over mature stage of shale. With the increase of formation pressure, the micropore volume decreases slightly, the mesopore volume increases significantly, and the macropore volume changes have two stages.

The current work introduces a new class of fuzzy soft B continuous functions such as slightly b continuous, semi b continuous, pre b continuous functions and their relation withthe existing fuzzy soft continuous functions in fuzzy soft topological spaces. Further optimal definitions of totally b continuous functions have also been brought out in the paper. A new space such as fuzzy soft b compact space is also initiated.