A Class of Spaces Containing all Connected and all Locally Connected Spaces

The Structure of Locally Connected Topological Spaces

0.1. This paper presents an investigation of the following problem. Exhibit a class X of topological spaces which contains all peano spaces and which has the following properties: (1) a cyclic element theory exists in each space of the class, (2) the abstract set consisting of all cyclic element of any space X of the class can be topologized so as to be a member of the class X, and (3) the hype...

Connected and Hyperconnected Generalized Topological Spaces

A. Csaszar introduced and extensively studied the notion of generalized open sets. Following Csazar, we introduce a new notion hyperconnected. We study some specic properties about connected and hyperconnected in generalized topological spaces. Finally, we characterize the connected component in generalized topological spaces.

One Dimensional Locally Connected S - spaces ∗ Joan

We construct, assuming Jensen’s principle ♦, a one-dimensional locally connected hereditarily separable continuum without convergent sequences.

One Dimensional Locally Connected S - spaces ∗

We construct, assuming Jensen’s principle ♦, a one-dimensional locally connected hereditarily separable continuum without convergent sequences.

Soft Connected Spaces and Soft Paracompact Spaces