26 November 2014

16:00

Leobardo Fernández Román

Abstract

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:

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}.

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}.

Also, it is possible to define the arcwise

connected version of these functions.

Given an arcwise connected continuum X:

Ta:P(X) to P(X) given by, for each A in P(X),

Ta(A) = X \ { x in X : there is an arcwise

connected continuum W such that x is in

Int(W) and W does not intersect A}.

Ka:P(X) to P(X) given by, for each A in P(X),

Ka(A) = Intersection{ W : W is an arcwise

connected subcontinuum of X and A is in

the interior of W}

Some properties, examples and relations

between these functions are going to be

presented.