Background Sober living houses (SLHs) are peer-managed residences that require sobriety and household participation among residents who rent rooms on a monthly (indefinite) basis and otherwise live normal lives according to personal schedules and needs. The houses do not provide counseling or services, but regular attendance at 12-step or other types of mutual-help groups is generally required....

In this paper we define $q$-spherical surfaces as the that contain absolute conic of Euclidean space a $q-$fold curve. Particular attention is paid to with singular points highest order. Two classes such surfaces, one and two $n-$fold points, are discussed in detail. We study their properties, give algebraic equations visualize them program {\it Mathematica}.

Considering a countable number of topologies on a set X, we introduce the notion of (א0)topological spaces as a generalization of the notions of both bitopological spaces and (ω)topological spaces, and study some of their properties. AMS Mathematics Subject Classification (2000): 54A10

In this paper we define pairwise-$\alpha$-paracompact subsets as a generalisation of $\alpha$-paracompact in topological spaces and study their properties its relations with other bitopological spaces. Several theorems are obtained concerning sets. We introduced the definition $p$-paracompact bitoplogical