@article{KARIMPOUR_1991, title={COMPLEMENTARY TOPOLOGY AND BOOLEAN RING}, volume={22}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4561}, DOI={10.5556/j.tkjm.22.1991.4561}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">A topology $\tau$</span> <span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">on a set $X$ is called Complementary topology if for each open set $U$ in</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">-$\tau$, </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">its Complement $X-U$ is also in $\tau$</span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">. </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">Since Complementary topologies are the only topologies that form </span><span style="font-size: 9.000000pt; font-family: ’TimesNewRomanPSMT’;">a </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">Boolean ring under the usual operations. These topologies are characterized. The paper then concentrates on the determination of the ideals and maximal ideals of such a ring. </span></p> </div> </div> </div>}, number={1}, journal={Tamkang Journal of Mathematics}, author={KARIMPOUR, RAHIM G.}, year={1991}, month={Mar.}, pages={1–5} }