Concerning RICG I, 194 A and its metric form

A Puzzle concerning Matter and Form

Metric Considerations concerning the Mixed Littlewood Conjecture

The main goal of this note is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan-Teulié Conjecture – also known as the ‘Mixed Littlewood Conjecture’. Let p be a prime. A consequence of our main result is that, for almost every real number α lim inf n→∞ n(log n)|n|p ‖nα‖ = 0 . Mathematics Subject Classification 2000: 11J83, 11J25, 11K55, 11K60

Some Remarks concerning D – Metric Spaces

In this note we make some remarks concerning D–metric spaces, and present some examples which show that many of the basic claims concerning the topological structure of such spaces are incorrect, thus nullifying many of the results claimed for these spaces.

A new form of the C - metric

The usual form of the C-metric has the structure function G(ξ) = 1 − ξ 2 − 2mAξ 3 , whose cubic nature can make calculations cumbersome, especially when explicit expressions for its roots are required. In this paper, we propose a new form of the C-metric, with the explicitly factorisable structure function G(ξ) = (1 − ξ 2)(1 + 2mAξ). Although this form is related to the usual one by a coordinat...

A few remarks concerning complex-analytic metric spaces

Let E be a closed set in C, normally with empty interior, and let us consider continuously-differentiable functions on E in the sense of Whitney, in which the differential of the function is automatically included. This means a continuous complex-valued function f(z) on E together with a real-linear mapping dfz : C n → C defined and continuous for z ∈ E, with properties like those of an ordinar...