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...

Introduction. In his monograph [l], Császár introduced the notion of a syntopogenous space, which generalized the notions of a topological space, a proximity space, and a uniform space. Although Császár was able to obtain many of the usual theorems of general topology in this more general setting, the basic topological notion of connectedness was not introduced at all. Mrówka and Pervin [2] hav...

We study asset pricing in economies with large information networks. We derive closed form expressions for price, volatility, profitability and several other key variables, as a function of the network topology. We focus on networks that are sparse and have power law degree distributions, in line with empirical studies of large scale social networks. Our analysis allows us to rank information n...

In this paper, we characterize both closed and strongly subobjects in the category of bounded uniform filter spaces introduce two notions closure operators which satisfy weakly hereditary, idempotent productive properties. We further each Tj (j= 0,1) using these examine that them form quotient-reflective subcategories spaces. Also, connected Finally, ultraconnected objects topological relations...