The set functions T, K and S.

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