This study introduce a new type of closed sets in topology called Generalized h-closed (briefly, gh-closed) define as follow: E ⊆ χ be gh-closed set if CLh (E)⊆ U whenever and is open (χ,τ). The relation between other classes ( h-closed, g-closed, g -closed, g-closed αg-closed) are studied. Also, the notion gh-continuous mapping on topological space some properties proved. Finally, separation a...

The notions of int-soft filters, int-soft G-filters, regular int-soft filters, and MV-int-soft filters in residuated lattices are introduced, and their relations, properties, and characterizations are investigated. Conditions for an int-soft filter to be an int-soft G-filter, a regular int-soft filter, or an MV-int-soft filter are provided. The extension property for an int-soft G-filter is dis...

We introduce a new class of sets namely \((1, 2)^\star\)-\(\check{g}_\alpha\)-closed sets, 2)^\star\)-\(\Lambda_{\mathcal{G}}\)-set, 2)^\star\)-\(\lambda_{\mathcal{G}}\)-set and 2)^\star\)-\(\check{g}_\alpha\)-Locally closed are study in bitopological spaces. prove that this classes lies between 2)^\star\)-\(\alpha\)-closed 2)^\star\)-\(\alpha g\)-closed sets. Furthermore, we discuss some essen...