Criteria for metrisability

Metrisability of Unions of Spaces

Partial metrisability of continuous posets

In this article, we characterise all continuous posets which are partially metrizable in their Scott topology. We present conditions for pmetrizability, which are both necessary and sufficient, in terms of measurements, domain-theoretic bases and, in a more general setting, in terms of radially convex metrics. These conditions, together with their refinements and generalisations, set a natural ...

Metrisability of Two-dimensional Projective Structures

We carry out the programme of R. Liouville [18] to construct an explicit local obstruction to the existence of a Levi–Civita connection within a given projective structure [Γ] on a surface. The obstruction is of order 5 in the components of a connection in a projective class. It can be expressed as a point invariant for a second order ODE whose integral curves are the geodesics of [Γ] or as a w...

Local Symmetry and Triangle Laws Are Sufficient for Metrisability

There is a long history in which attempts have been made to weaken the conditions defining a metric function whilst retaining metrisability. In this note, we survey some of our recent results in this context, deduce some well-known metrisation theorems, and present some related unsolved problems. Some of the more important early papers on this topic were by E. W. Chi t ten den (see, for example...

Criteria for evaluating technology leaders in schools: Mixed research

The goal of this research was to extract criteria for evaluating technology leaders and it was conducted by mixed method.  The research method was descriptive in the qualitative part and survey method in the quantitative part.  The research was carried out in smart and semi-smart  primary schools in Zanjan province in the academic year of 1398-99. Participants of the qualitative part were fifte...