Proto-metrisable spaces are elastic

On Locally Compact Metrisable Spaces

In Theorem 1 the word metric may be replaced, on the one hand, by regular, on the other, by complete metric. This theorem is of interest chiefly because of the similar well known characterizations of the class of all compact metrisable spaces and of the class of all metrisable spaces which are homeomorphic to complete metric spaces.§ The method of proof also relates it to the two characterizati...

Proto-metrizable fuzzy topological spaces

Discrete Time Elastic Vector Spaces

This paper proposes a framework dedicated to the construction of what we call time elastic inner products allowing one to embed sets of non-uniformly sampled multivariate time series of varying lengths into vector space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our f...

Completely metrisable groups acting on trees

We consider actions of completely metrisable groups on simplicial trees in the context of the Bass–Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any d...

Are activated proto-onc genes cancer genes?

The main objective of cancer molecu~ar biology is to identity cancer genes. ~espite fierce efforts, this objective has still not been met [1-3]. As yet the only known cancer genes are the transformin~ one g~n.e~ of retroviruses. Typically these VIruses InItiate and maintain cancers with autonomous transforming genes that ~re domina~t in susceptible cells [5]. The dIsc~very of ~Ingle gene determ...