@article{EL-MONSEF_KOZAE_ABO-KHADRA_1993, title={EXTENSIONS GENERATED BY CLOSED SETS}, volume={24}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/4488}, DOI={10.5556/j.tkjm.25.1994.4488}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">From the nonempty collection of all closed sets $</span><span style="font-size: 11.000000pt; font-family: ’Arial’; font-style: italic;">(Y)$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">of any topological space $(X , \tau</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">)$, </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">Schmidt generates a topological space $</span><span style="font-size: 12.000000pt; font-family: ’TimesNewRomanPSMT’;">(Y,\mathcal{U}</span><span style="font-size: 11.000000pt; font-family: ’Arial’; font-style: italic;">)$. </span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPSMT’;">In </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">this paper, we give some properties of this topological space. We determined when $</span><span style="font-size: 11.000000pt; font-family: ’Arial’; font-style: italic;">(f,(Y,\mathcal{U}))$ </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">is an extension of $(X , \tau</span><span style="font-size: 11.000000pt; font-family: ’TimesNewRomanPS’; font-style: italic;">)$. </span><span style="font-size: 10.000000pt; font-family: ’TimesNewRomanPSMT’;">Also we give some separation properties. This paper leads us to unsolved problem men- tioned at the encl of it. </span></p> </div> </div> </div>}, number={2}, journal={Tamkang Journal of Mathematics}, author={EL-MONSEF, M. E ABD and KOZAE, A. M. and ABO-KHADRA, A. A.}, year={1993}, month={Jun.}, pages={189–193} }