Approximating continua from within

From continua to R-trees

We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X . AMS Classification 54F15,54F05,20F65,20E08

Approximating Visibility Problems within a Constant

Visibility problems deal with placing a minimum number of transmitting stations in a region thus covering a maximum number of communication needs. Here we investigate some variants of such problems e.g. i) given a polygon P with weights on the vertices find at most k convex subpolygons Ci of P (possibly overlapping) with V (Ci) ⊆ V (P) so that the weight of the vertices is a maximum, and ii) gi...

Approximating the Svp to within a Factor ?

Exactly two-to-one maps from continua onto some tree-like continua

It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua ...

Hemicrania Continua.

Hearing the diagnosis of hemicrania continua can seem as if the medical provider is stating the obvious, because the name in Latin means that half of the head hurts. However, hemicrania continua is a unique type of headache, one that by definition responds to 1 medication, indomethacin. Hemicrania continua is usually referred to by its initials, HC. While HC is not seen as frequently as migrain...