Extending families of disjoint zero sets

Almost disjoint families of connected sets

We investigate the question which (separable metrizable) spaces have a ‘large’ almost disjoint family of connected (and locally connected) sets. Every compact space of dimension at least 2 as well as all compact spaces containing an ‘uncountable star’ have such a family. Our results show that the situation for 1-dimensional compacta is unclear.  2004 Elsevier B.V. All rights reserved.

Almost disjoint families on large underlying sets

We show that, for any poset P, the existence of a P-indestructible mad family F ⊆ [ω]א0 is equivalent to the existence of such a family over אn for some/all n ∈ ω. Under the very weak square principle ¤∗∗∗ ω1,μ of Fuchino and Soukup [7] and cf([μ]א0 ,⊆) = μ+ for all limit cardinals μ of cofinality ω, the equivalence for any proper poset P transfers to all cardinals. That is, under these assumpt...

Disjoint Common Partial Transversals of Two Families of Sets

Complete Sets of Disjoint Difference Families and their Applications

Let G be an abelian group. A collection of (G, k, λ) disjoint difference families, {F0,F1, · · · ,Fs−1}, is a complete set of disjoint difference families if ∪0≤i≤s−1∪B∈FiB form a partition of G− {0}. In this paper, several construction methods are provided for complete sets of disjoint difference families. Applications to one-factorizations of complete graphs and to cyclically resolvable cycli...

Degrees of M-fuzzy families of independent L-fuzzy sets

The present paper studies fuzzy matroids in view of degree. First wegeneralize the notion of $(L,M)$-fuzzy independent structure byintroducing the degree of $M$-fuzzy family of independent $L$-fuzzysets with respect to a mapping from $L^X$ to $M$. Such kind ofdegrees is proved to satisfy some axioms similar to those satisfiedby $(L,M)$-fuzzy independent structure. ...