When counting isomers with a given number of atoms one usually assumes that we want to count (connected) molecules. In this note we present a method that can be used for counting disconnected structures if counts of connected structures are given. The method can be used also in the reverse direction. If the numbers of all structures are known, the number of connected structures can be readily d...

Disconnected pancreatic duct syndrome (DPDS) is characterised by disruption of the main pancreatic duct with a loss of continuity between the pancreatic duct and the gastrointestinal tract caused by ductal necrosis after severe acute necrotising pancreatitis treated medically, by percutaneous drainage, or necrosectomy. There are no clear epidemiological data on the real incidence of DPDS; appro...

Very often in analysis, one focuses on connected spaces. This is certainly not always the case, and in particular there are many interesting matters related to Cantor sets. Here we are more concerned with a type of complementary situation. As a basic scenario, suppose that U is an open set in Rn and that E is a closed set contained in the boundary of U such that for every x ∈ U and r > 0 there ...

For a connected graph G = (V,E), a subset U ⊆ V is called a disconnected cut if U disconnects the graph and the subgraph induced by U is disconnected as well. A natural condition is to impose that for any u ∈ U the subgraph induced by (V \U)∪{u} is connected. In that case U is called a minimal disconnected cut. We show that the problem of testing whether a graph has a minimal disconnected cut i...

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...