1 research outputs found
Boundary-Border Extensions of the Kuratowski Monoid
The Kuratowski monoid is generated under operator composition by
closure and complement in a nonempty topological space. It satisfies
. The Gaida-Eremenko (or GE) monoid
extends by adding the boundary operator. It satisfies
. We show that when the GE monoid
is determined by . When if the interior of the
boundary of every subset is clopen, then . This defines a new
type of topological space we call . Otherwise
. When applied to an arbitrary subset the GE monoid collapses
in one of possible ways. We investigate how these collapses and
interdepend, settling two questions raised by Gardner and
Jackson. Computer experimentation played a key role in our research.Comment: 48 pages, 9 figure