In this article we established the concept of multi-continuity in minimal structure spaces (in short $\mathscr{M}$ space) and notion product space multiset topological space. Continuity between $\mathscr{M}$-space, generalized topology ideal spaces. We have investigated some basic properties $\mathscr{M}$–continuity space, such as composition $\mathscr{M}$–continuous functions, functions etc.

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...