Small designs for path-connected spaces and path-connected homogeneous spaces

Small Designs for Path Connected Spaces and Path Connected Homogeneous Spaces

We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of ndesigns on S of size Od(n d log(n)d−1).

Spaces That Are Connected but Not Path-connected

A topological space X is called connected if it’s impossible to write X as a union of two nonempty disjoint open subsets: if X = U ∪ V where U and V are open subsets of X and U ∩ V = ∅ then one of U or V is empty. Intuitively, this means X consists of one piece. A subset of a topological space is called connected if it is connected in the subspace topology. The most fundamental example of a con...

Homogeneous Countable Connected Hausdorff Spaces

In 1925, P. Urysohn gave an example of a countable connected Hausdorff space [4]. Other examples have been contributed by R. Bing [l], M. Brown [2], and E. Hewitt [3]. Relatively few of the properties of such spaces have been examined. In this paper the question of homogeneity is studied. Theorem I shows that there exists a bihomogeneous countable connected Hausdorff space. Theorems II and III ...

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.

Soft Connected Spaces and Soft Paracompact Spaces