HYPERCONNECTEDNESS MODULO AN IDEAL
Abstract
In this paper, hyperconnectedness with respect to an ideal, called
hyperconnectedness modulo an ideal, of a topological space X is introduced.
It is shown that hyperconnectedness and hyperconnectedness modulo an ideal
coincide in case of trivial and codense ideal. Several characterisations of hy-
perconnectedness modulo I are obtained using semi-open, pre-open and semi-
preopen sets. It is also shown that I-hyperconnectedness and hyperconnect-
edness modulo I, where I is an ideal in space X, are equivalent. A new type
of semi-open modulo ideal sets are dened and several characterisations of
hyperconnectedness modulo an ideal using these sets are obtained.