This year, we introduced the concept of infra soft topology as a new generalization topology. To complete our analysis this space, devote paper to presenting concepts connected and locally spaces. We provide some descriptions for connectedness elucidate that there is no relationship between an topological space its parametric spaces with respect property connectedness. discuss behaviors under h...

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...