In ref. [l], Mauldin et al. proved a theorem which at first sight may seem slightly paradoxical but we perceive as exceedingly interesting. This theorem states that the Hausdorff dimension dy’ of a randomly constructed Cantor set is d:’ = @, where $ = (d5 1)/2 is the G o Id en Mean. That such disordered indeterministic construction which actually epitomize dissonance should single out the Golde...

A = Γ\β<a {%x is an acculumation point of A and x e A}. Recall that a subset, H, of a Polish space is scattered if, and only if H is a countable Gδ set, or equivalently, there is a countable ordinal 7 such that the 7th Cantor-Bendixson derived set, H\ of H is empty [5]. By the Cantor-Bendixson order of a subset H of a topological space is meant the first ordinal 7 such that H = H. The Cantor-Be...

We prove that if V = L then there is a Π11 maximal orthogonal (i.e. mutually singular) set of measures on Cantor space. This provides a natural counterpoint to the well-known Theorem of Preiss and Rataj [16] that no analytic set of measures can be maximal orthogonal.

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...

A simple proof is presented for the min-max theorem of Lovv asz on cacti. Instead of using the result of Lovv asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem.