A Whitney map onto the Long Arc

In a recent paper, Garc\'{\i}a-Velazquez has extended the notion of Whitney map to include maps with non-metrizable codomain and left open the question of whether there is a continuum that admits such a Whitney map. In this paper, we consider two examples of hereditarily indecomposable, chainable continua of weight $\omega_1$ constructed by Michel Smith; we show that one of them admits a Whitney function onto the long arc and the other admits no Whitney maps at all

Far points and discretely generated spaces

We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this, we study the cardinal number given by the smallest possible character of remote and far sets of separable metrizable spaces. Finally, we prove that in some cases a countable space has far points

Complete confined bases for beam propagation in Cartesian coordinates

Complete bases that are useful for beam propagation problems and that present the distinct property of being spatially confined at the initial plane are proposed. These bases are constructed in terms of polynomials of Gaussians, in contrast with standard alternatives such as the Hermite-Gaussian basis that are given by a Gaussian times a polynomial. The property of spatial confinement implies that, for all basis elements, the spatial extent at the initial plane is roughly the same. This property leads to an optimal scaling parameter that is independent of truncation order for the fitting of a confined initial field. Given their form as combinations of Gaussians, the paraxial propagation of these basis elements can be modeled analytically.Comment: 6 pages, 4 figures, \c{opyright} 2017 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite