Introduction, Let © be the class of all countable and connected perfectly separable Hausdorff spaces containing more than one point. I t is known that an ©-space cannot be regular or compact. Urysohn, using a complicated identification of points, has constructed the first example of an ©-space. Two ©-spaces, X and X*, more simply constructed and not involving identifications, are presented here...

Anderson and Canary ([1]) have constructed examples of 3-manifolds M for which the space of convex co-compact representations of π1(M) in PSL2(C) is disconnected but has connected closure (in the topology of algebraic convergence). More precisely, they showed that for their examples the intersection of the closures of any two path components of the space of convex co-compact representations is ...

A relational structure is called reversible iff every bijective endomorphism of that an automorphism. We characterize property in the class disconnected binary structures, and one its subclasses—posets are disjoint union chains. Also, using concept a monotone function from structures preordered by monomorphism into well founded relation, we detect additional classes posets. further give equival...

In this paper, a supervisory controller is proposed to manage the power flow in a hybrid AC/DC micro-grid for both grid-connected and disconnected modes. When the hybrid AC/DC micro-grid is connected to the utility grid, power surplus or shortage leads to power trade between the micro-grid and the utility grid. In the grid-disconnected mode, the renewable power sources (wind and solar generatio...