Uniformly Movable Categories and Uniform Movability of Topological Spaces

Abstract

A categorical generalization of the notion of movability from the inverse systems and shape theory was given by the first author who defined the notion of movable category and interpreted by this the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of the shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is a uniformly movable category. This is a weakened version of the categorical notion of uniform movability introduced by the second author.

Thermohydrodynamics of boiling in a van der Waals fluid

“…FEMLEGO is a symbolic tool that defines the differential equations, boundary conditions, initial conditions, and the method of solving each equation in a single MAPLE worksheet. It also inherits adaptive mesh refinement capabilities [26], which are used in these simulations. This enables us to have a high resolution of the interface without spending excessive computational time.…”

“…At the next refinement step, elements containing hanging nodes are marked for refinement. The refinement or derefinement stops if and only if no element is marked for refinement or de-refinement (see [26]). All variables are discretized in space using piecewise linear functions.…”

Strong movable categories and strong movability of topological spaces

“…This approach is based on some ideas applied in [2], [5] to the movability of topological spaces. As it shown in [6] and [10], the same ideas are applicable also for studying the uniform movability of topological spaces.…”

“…it remains to see that the homotopy class η ′′ : X α ′ → Q ′′ satisfies the equalities ( 6) and (7). Indeed (6) follows from (20), (17), ( 18) and ( 14):…”