An example of maximal connected Hausdorff space

Connected Hausdorff subtopologies

A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable π-weight and no connected, Hausdorff subtopology is provided.

Connected Mappings of Hausdorff Spaces

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 ...

The maximal total irregularity of some connected graphs

The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.

the maximal total irregularity of some connected graphs

the total irregularity of a graph g is defined as 〖irr〗_t (g)=1/2 ∑_(u,v∈v(g))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈v(g). in this paper by using the gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices.