Constructing uniform spaces

Constructing Smooth Loop Spaces

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions for the model space which, if satisfied, mean that a smooth structure exists. We also show how various desired properties can be derived from the model spac...

Constructing Common Information Spaces

This paper investigates an important, yet under-researched topic in CSCW, namely shared, or common, information spaces. We provide some background to work in the area, and then proceed to examine features of such spaces. The work involved in both putting information in common, and in interpreting it, has often not been sufficiently recognized. Through a number of situations we discuss the influ...

Constructing common information spaces

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

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...

On statistical type convergence in uniform spaces

The concept of ${mathscr{F}}_{st}$-fundamentality is introduced in uniform spaces, generated by some filter ${mathscr{F}}$. Its equivalence to the concept of ${mathscr{F}}$-convergence in uniform spaces is proved. This convergence generalizes many kinds of convergence, including the well-known statistical convergence.