The Schelling model describing segregation between two groups of residential agents, reflects the most abstract, basic view of noneconomic forces motivating residential migrations: be close to people of ‘‘your own’’ kind. The model assumes that residential agents, located in neighborhoods where the fraction of ‘‘friends’’ is less than a predefined threshold value F, try to relocate to neighborh...

These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in mani...

At a time when so much violence is taking place in society and in the world, we search for some ways to make things better. Unexpectedly, current research indicates that the strategic use of the natural environment, in particular open spaces referred to as greenspace, has the potential to reduce violence in urban neighborhoods (Younan et al, 2016). This information is most welcome, and is furth...

We investigate the dynamic relationship between residential choices of individuals and resulting long-term aggregate segregation patterns, allowing for feedback effects of macrolevel neighborhood conditions on residential choices. We reinterpret past survey data on whites' attitudes about desired neighborhoods as revealing large heterogeneity in whites' tolerance of black neighbors. Through age...