Past Analytic Topology in Mathematics and Computer Science

29 October 2014
14:00
Robin Knight
Abstract

Counterexamples to Vaught's Conjecture regarding the number of countable
models of a theory in a logical language, may felicitously be studied by investigating a tree
of types of different arities and belonging to different languages. This
tree emerges from a category of topological spaces, and may be studied as such, without
reference to the original logic. The tree has an intuitive character of absoluteness
and of self-similarity. We present theorems expressing these ideas, some old and some new.

  • Analytic Topology in Mathematics and Computer Science
22 October 2014
16:00
Robert Leek
Abstract
 
Using an internal characterisation of radiality or
> Fréchet-Urysohness, we can translate this property into other structural
> forms for many problems and classes of spaces. In this talk, I will
> recap this internal characterisation and translate the properties of
> being radial / Fréchet-Urysohn (Stone-Čech, Hewitt) into the prime ideal
> structure on C*(X) / C(X) for Tychonoff spaces, with a view to reaching
> out to other parts of algebra, e.g. C*-algebras, algebraic geometry, etc.
  • Analytic Topology in Mathematics and Computer Science
18 June 2014
16:00
Leobardo Fernandez Ramon
Abstract
<p><span>&nbsp;A continuum is a non-empty compact connected metric space. Given a continuum X let P(X) be the power set of X. We define the following set functions:</span><br /><span>T:P(X) to P(X) given by, for each A in P(X), T(A) = X \ { x in X : there is a continuum W such that x is in Int(W) and W does not intersect A}</span><br /><span>K:P(X) to P(X) given by, for each A in P(X), K(A) = Intersection{ W : W is a subcontinuum of X and A is in the interior of W}</span><br /><span>S:P(X) to P(X) given by, for each A in P(X), S(A) = { x in T(A) : A intersects T(x)}</span><br /><span>Some properties and relations between these functions are going to be presented.</span></p>
  • Analytic Topology in Mathematics and Computer Science

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