On the continuity of Professor Jones' set function K
by
Sergio Macias
National University of Mexico

A continuum is a nonempty compact, connected Hausdorff space. Given a continuum X, we define Professor Jones' sets functions T and K as follows: If A is a subset of X, then

T(A)={a ∈ X | if W is a subcontinuum of X such thatx ∈ Int(W), then W∩A ≠ ∅}

and

K(A)=∩{W | W is a subcontinuum of X such that A ⊂ Int(W)}.

Professor David P. Bellamy asked, If T is continuous for a continuum X, is K also continuous for X? We present a class of continua for which the answer to this question is positive.

Date received: February 4, 2010