Squeezing the Sierpinski sponge

Analysis on the Sierpinski Carpet

The ‘analysis on fractals’ and ‘analysis on metric spaces’ communities have tended to work independently. Metric spaces such as the Sierpinski carpet fail to satisfy some of the properties which are generally assumed for metric spaces. This survey discusses analysis on the Sierpinski carpet, with particular emphasis on the properties of the heat kernel. 1. Background and history Percolation was...

Sampling on the Sierpinski Gasket

Was Sierpinski Right? IV

We prove for any μ = μ < θ < λ, λ large enough (just strongly inaccessible Mahlo) the consistency of 2 = λ → [θ]23 and even 2 μ = λ → [θ]2σ,2 for σ < μ. The new point is that possibly θ > μ. Typed 5/92 (20 , k 2 -Mahlo,λ → [א2]23; some on models) I thank Alice Leonhardt for the beautiful typing. Latest Revision 2012/Oct/24 Revised and Expanded 5/94 based on lectures, Summer ’94, Jerusalem. Part...

Locally Sierpinski Quotients

Given any non-trivial, connected topological space X, it is possible to define an equivalence relation ∼ on it such that the topological quotient space X/ ∼ is the Sierpinski space. Locally Sierpinski spaces are generalizations of the Sierpinski space and here we address the following question. Does a statement like the one above hold if Sierpinski is replaced by (proper) locally Sierpinski ? T...

Squeezing arguments

Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s ...