CL(R) is simply connected under the Vietoris topology

The connected Vietoris powerlocale

The Vietoris powerlocale V X is a point-free analogue of the Vietoris hyperspace. In this paper we introduce and study a sublocale V X whose points are those points of V X that (considered as sublocales of X) satisfy a constructively strong connectedness property. V c is a strong monad on the category of locales. The strength gives rise to a product map × : V X × V Y → V (X × Y ), showing that ...

Near { Cohomology of Hilbertcomplexes and Topology Ofnon { Simply Connected Manifolds

On digital simply connected spaces and manifolds: a digital simply connected 3-manifold is the digital 3-sphere

In the framework of digital topology, we study structural and topological properties of digital ndimensional manifolds. We introduce the notion of simple connectedness of a digital space and prove that if M and N are homotopy equivalent digital spaces and M is simply connected, then so is N. We show that a simply connected digital 2-manifold is the digital 2-sphere and a simply connected digita...

Some results of semilocally simply connected property

If we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. In this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

On Simply-connected 4-manifolds

This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and...