Concerning semi-local-connectedness and cutting in nonlocally connected continua

Concerning Aposyndetic and Non-aposyndetic Continua

Introduction. One might judge from the title that I am going to discuss continua. For is not a continuum either aposyndetic or nonaposyndetic? What I intend to do is to consider continua from a certain point of view, and from this point of view continua may be classified in a rough sort of way. This system of classification (and the basic concept upon which it rests) is only in its infancy. Her...

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Concerning the Cut Points of Continua*

In this paper propositions will be established concerning the collection of all the cut points of a given planef continuum. It will be shown that there does not exist an uncountable collection of mutually exclusive subcontinua of a given continuum M each of which contains at least one cut point of M. With the aid of this fundamental theorem it is shown, among other things, that the set of all t...

CONCERNING INTERSECTING CONTINUA BY R. L. MooRu

Hamiltonian connectedness in 3-connected line graphs

We investigate graphs G such that the line graph L(G) is hamiltonian connected if and only if L(G) is 3-connected, and prove that if each 3-edge-cut contains an edge lying in a short cycle of G, then L(G) has the above mentioned property. Our result extends Kriesell’s recent result in [J. of Combinatorial Theory, Ser. B. 82 (2001), 306-315] that every 4-connected line graph of a claw free graph...