In this paper, the concepts of LωH-sets and LωH-closed spaces are proposed in Lω-spaces by means of (αω)−-remote neighborhood family. The characterizations of LωH-sets and LωH-closed spaces are systematically discussed. Some important properties of LωH-closed spaces, such as the LωH-closed spaces is ω-regular closed hereditary, arbitrarily multiplicative and preserving invariance under almost (...

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling supporting $1$-Poincaré inequality. We show that at almost every point $x$ outside Cantor and jump parts function, limit function is Lipschitz continuous least gradient on tangent space to based $x$. also that, co-dimension $1$ Hausdorff measure-theoretic boundary set $E$ ...