Introduction 1. Definitions and Elementary Results 2. When Disconnected Filled-in Julia Sets are Cantor Sets 3. Smooth Julia Sets 4. Fixed Points 5. Remarks on the Topology of the Connectedness Locus Acknowledgements References We consider the rational maps given by z jzj z c, for z and c complex and fixed and real. The case corresponds to quadratic polynomials: some of the well-known results f...

We investigate the computational complexity of spatial logics extended with the means to represent topological connectedness and restrict the number of connected components. In particular, we show that the connectedness constraints can increase complexity from NP to PSpace, ExpTime and, if component counting is allowed, to NExpTime.

We study the probability of connectedness for structures of size n when all components must have size at least m: In the border between almost certain connectedness and almost certain disconnectedness, we encounter a generalized Buchstab function of n=m: r 2004 Elsevier Inc. All rights reserved.

According to the association-induction hypothesis, the core of living phenomena lies in the long-range, one-on-many connectedness among all three major components of living protoplasm: protein, water and K+ (and the controlling agents, called the cardinal adsorbents.) This article describes simple experimental models that could cogently test the theory of this connectedness and its control by d...

In this paper, a certain new connectedness of L-fuzzy subsets inL-topological spaces is introduced and studied by means of preclosed sets. Itpreserves some fundamental properties of connected set in general topology.Especially the famous K. Fan’s Theorem holds.

In recent years, an interesting class of communication systems has emerged: Social Awareness (SA) Systems. These systems aim at increasing people’s sense of social connectedness by providing them with peripheral awareness of information about people from their social network (e.g. presence, availability, activities). The interaction principles of these systems are based on the paradigms of Ubiq...

We define direct sums and a corresponding notion of con-nectedness for graph limits. Every graph limit has a unique decomposition as a direct sum of connected components. As is well-known, graph limits may be represented by symmetric functions on a probability space; there are natural definitions of direct sums and connectedness for such functions, and there is a perfect correspondence with the...

The Centre for Market and Public Organisation (CMPO) is a leading research centre, combining expertise in economics, geography and law. Our objective is to study the intersection between the public and private sectors of the economy, and in particular to understand the right way to organise and deliver public services. The Centre aims to develop research, contribute to the public debate and inf...

A notion of connectedness with respect to a closure operator C and a class of monomorphisms N is introduced in an arbitrary category X . It is shown that under appropriate hypotheses, most classical results about topological connectedness can be generalized to this setting. Examples that illustrate this new concept are provided. Mathematics Subject Classification (1991). 18D35, 06A15, 54D05.

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133...