An extension that nowhere has the Fréchet property.

Nowhere dense graph classes, stability, and the independence property

A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of cliques that occur as (topological) r-minors. We observe that this tameness notion from algorithmic graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence pr...

Annotations of an Example That Markov Process Has No Strong Markov Property

In this paper, we discuss an incorrect example that a Markov process does not satisfy strong Markov property, and analyzes the reason of mistake. In the end, we point out it is not reasonable to define strong Markov property by using transition probability functions since transition probability functions might not be one and only.

When the extension property does not hold

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with a noncyclic socle.

The ¿-norm Extension Property for Banach Spaces1

Graphs with the cycle extension property

A connected graph G is said to have the cycle extension property (or more briefly, “G is CEP”) if it contains a 2-factor and for every cycle C in G with |V (C)| ≤ |V (G)| − 3, there is a 2-factor FC in G which includes C. We characterize all graphs which are CEP.