More about maximal (n, r)-sets

ATOMLESS r-MAXIMAL SETS

We focus on L(A), the filter of supersets of A in the structure of the computably enumerable sets under the inclusion relation, where A is an atomless r-maximal set. We answer a long standing question by showing that there are infinitely many pairwise non-isomorphic filters of this type.

Some results on maximal open sets

In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.

Maximal independent sets in graphs with at most r cycles

We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with n vertices Contract grant sponsor: Award from DIMACS (partially; to V.R.V.); Contract grant sponsor: NSF VIGRE grant to the Rutgers University Department of Mathematics (partially; to V.R.V.). Journal of Graph Theory © 2006 Wiley Periodicals, Inc. 270 MAXIMAL INDEPENDEN...

ON MAXIMAL IDEALS OF R∞L

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...

Concerning Maximal Sets