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 hyperconnectedness modulo an ideal I are obtained using semi-open, pre-open and semi-preopen sets. It is also shown that I-hyperconnectedness and hyperconnectedness modulo I, where I is an ideal in a space X, are equivalent. A new type of semi-open modulo ideal sets are defined and several characterisations of hyperconnectedness modulo an ideal using these sets are obtained.
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