What does the term regularity mean? - Mathematics Stack Exchange The regularity a solution can inherit depends on the properties of the problem, i e , the smoothness of a domain boundary, the smoothness of boundary conditions and initial data Notice here that the smoothness of the initial data falls under the category of "regularity of initial data"
set theory - Help understanding the axiom of regularity - Mathematics . . . Usual mathematical results (like propositions on analysis and geometry) would not need the axiom of regularity, but some deeper set theory heavily relies on the axiom of regularity As a side note, a regularity-free proof of "the existence of a basis on any vector spaces implies AC" is not known $\endgroup$ –
regularity of a measure - Mathematics Stack Exchange Help save this proof about the regularity of the lebesgue measure on $\mathbb{R}^d$ 0 An example of a measure and of a set s t its measure cannot be approximated by measures of its open subsets
set theory - Axiom of Regularity - Mathematics Stack Exchange I am having difficulty understanding Axiom of Regularity : Every non-empty set $\\rm A$ contains an element $\\rm B$ which is disjoint from $\\rm A $ So from my understanding if I have a set like:
On the regularity of the boundary of an open set I'm considering the following regularity conditions for the boundary of $\Omega$: $\overline{\Omega}$ is a topological manifold with boundary (in other words, around each boundary point, $\Omega$ looks like a Euclidean half-space --up to homeomorphism)