In this paper, the definitions of novel classes generalized connected sets (briefly, g-Tg-connected sets) and disconnected g-Tg-disconnected in topological spaces Tg-spaces) are defined terms g-Tg -sets) and, their properties characterizations with respect to set-theoretic relations presented. The basic notions local, pathwise, local pathwise simple g-Tg-connectedness also study shows that -con...

The aim of this paper is to introduce the notions hereditarily disconnected and totally objects in a topological category examine relationship as well interrelationships between them. Moreover, we characterize each $T_{2}$, connected, disconnected, some categories compare our results with ones spaces.

A graph structure is deened on the Weyl groups. We show that these graphs are connected for Weyl groups of type An for n 4. 1. Introduction. We have deened a graph structure on Weyl groups through the root system associated with them. The planarity and the other properties of such graphs has been studied elsewhere (1] and 2]). The motivation for these graphs come from the method employed in pro...

We define direct sums and a corresponding notion of connectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric functions on a probability space; there are natural definitions of direct sums and connectedness for such functions, and there is a perfect correspondence with the ...