Distributed Computing in Monotone Topological Spaces

Abstract

In recent times, an alternate approach to model and analyze distributed computing systems has gained research attention. The alternate approach considers higher-dimensional topological spaces and homotopy as well as homology while modeling and analyzing asynchronous distributed computing. This paper proposes that the monotone spaces having ending property can be effectively employed to model and analyze consistency and convergence of distributed computing. A set of definitions and analytical properties are constructed considering monotone spaces. The inter-space relationship between simplexes and monotone in topological spaces is formulated.