Journal of Advanced Studies in Topology http://m-sciences.com/index.php?journal=jast <p style="text-align: justify;">The Journal of Advanced Studies in Topology (<strong>JAST</strong>) is dedicated to rapid publication of the highest quality short papers, regular papers, and expository papers.<span class="Apple-converted-space">&nbsp;</span><strong>JAST</strong><span class="Apple-converted-space">&nbsp;</span>is a peer-reviewed international journal, which publishes original research papers and survey articles in all aspects of topology and its applications.</p> Modern Science Publishers en-US Journal of Advanced Studies in Topology 2090-8288 <p>No manuscript should be submitted which has previously been published, or which has been simultaneously submitted for publication elsewhere. The copyright in a published article rests solely with the Modern Science Publishers, and the paper may not be reproduced in whole in part by any means whatsoever without prior written permission.</p> Soft almost $$\alpha$$-continuous mappings http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1415 <p>In the present paper the concept of soft almost $$\alpha$$-continuous mappings and soft almost $$\alpha$$-open mappings in soft topological spaces have been introduced and studied.</p> S. S. Thakur A. S. Rajput ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-08-10 2018-08-10 9 2 94 99 10.20454/jast.2018.1415 Weak and strong forms of fuzzy $$\alpha$$-open (closed) sets and its applications http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1411 <p>In this paper, we generalize the concept of infra-$$\alpha$$-open (closed) and supra-$$\alpha$$-open (closed) sets to fuzzy topological spaces and basic properties of these new concepts have been introduced. Some applications on fuzzy (supra-) infra-$$\alpha$$-open (closed) sets, likely, fuzzy (supra-) infra-$$\alpha$$-continuous mappings, fuzzy (supra-) infra-$$\alpha$$-open (closed) mappings, fuzzy supra-$$\alpha$$- irresolute mapping and fuzzy supra-$$\alpha$$-connected space are introduced. The relations and converse relations between these new concepts and others kinds of fuzzy open sets and fuzzy continuous mappings are discussed. Special results about these new concepts are investigated and studied.</p> Hakeem A. Othman Alanod M. Sibih ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-08-10 2018-08-10 9 2 100–112 100–112 10.20454/jast.2018.1411 Separation axioms on function spaces defined on bitopological spaces http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1454 <p>In this paper, we introduce separation axioms on the function space <em>p</em><em>− </em><em>C</em><em>ω</em>(<em>Y, Z</em>) and study how they relate<br>to separation axioms defined on the spaces (<em>Z, δ</em><em>i</em>) for <em>i </em>= 1<em>, </em>2, (<em>Z, δ</em>1<em>, δ</em>2), 1 <em>− </em><em>C</em><em>ς</em>(<em>Y, Z</em>) and 2 <em>− </em><em>C</em><em>ζ</em>(<em>Y, Z</em>). It<br>is shown that the space <em>p </em><em>− </em><em>C</em><em>ω</em>(<em>Y, Z</em>) is <em>p</em><em>T</em><em>◦</em>, <em>p</em><em>T</em>1, <em>p</em><em>T</em>2 and <em>p</em>regular, if the spaces (<em>Z, δ</em>1) and (<em>Z, δ</em>2) are both<br><em>T0</em>, <em>T</em>1, <em>T</em>2 and regular respectively. The space <em>p </em><em>− </em><em>C</em><em>ω</em>(<em>Y, Z</em>) is also shown to be <em>p</em><em>T0</em>, <em>p</em><em>T</em>1, <em>p</em><em>T</em>2 and <em>p</em>regular,<br>if the space (<em>Z, δ</em>1<em>, δ</em>2) is <em>p </em><em>− </em><em>T0</em>, <em>p </em><em>− </em><em>T</em>1, <em>p </em><em>− </em><em>T</em>2 and <em>p</em>-regular respectively. Finally, the space <em>p </em><em>− </em><em>C</em><em>ω</em>(<em>Y, Z</em>) is<br>shown to be&nbsp;<em>p</em><em>T0</em>, <em>p</em><em>T</em>1, <em>p</em><em>T</em>2 and <em>p</em>regular, if and only if the spaces 1 <em>− </em><em>C</em><em>ς</em>(<em>Y, Z</em>) and 2 <em>− </em><em>C</em><em>ζ</em>(<em>Y, Z</em>) are both <em>T</em>0,<br><em>T</em>1, <em>T</em>2, and only if the spaces 1 <em>− </em><em>C</em><em>ς</em>(<em>Y, Z</em>) and 2 <em>− </em><em>C</em><em>ζ</em>(<em>Y, Z</em>) are both regular respectively.</p> N. E. Muturi J. M. Khalagai G. P. Pokhariyal ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-08-22 2018-08-22 9 2 113 118 10.20454/jast.2018.1454 $$\alpha_\beta$$-Connectedness as a characterization of connectedness http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1401 <p>In this paper, a new class of $$\alpha_\beta$$-open sets in a topological space $$X$$ is introduced which forms a topology on $$X$$. The connectedness of this new topology on $$X$$, called $$\alpha_\beta$$-connectedness, turns out to be equivalent to connectedness of $$X$$ and hence also to $$\alpha$$-connectedness of $$X$$. The $$\alpha_\beta$$-continuous and $$\alpha_\beta$$-irresolute mappings are defined and their relationship with other mappings such as continuous mappings and $$\alpha$$-continuous mappings are discussed. An intermediate value theorem is obtained. The hyperconnected spaces constitute a subclass of $$\alpha_\beta$$-connected spaces.</p> B. K. Tyagi Manoj Bhardwaj Sumit Singh ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-09-25 2018-09-25 9 2 119 129 10.20454/jast.2018.1401 On irresolute topological rings http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1474 <p>In this paper we introduce a new type of a topological ring which is an irresolute topological ring (semi topological ring). The relation among of them are studied. Several results are given. In particular, in a semi Hausdorff space, we show that if a subring is commutative, then its semi closure commutative subring. Furthermore, we show that the center of a ring is semi closed.</p> Haval M. Mohammed Salih ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-10-26 2018-10-26 9 2 130 134 10.20454/jast.2018.1474 Pre-$$(\omega)$$separation axioms http://m-sciences.com/index.php?journal=jast&page=article&op=view&path%5B%5D=1492 <p>In this paper we use the notion of $$(\omega)$$ preopen sets to introduce and study pre-separation axioms in an<br>$$(\omega)$$topological space.</p> Rupesh Tiwari ##submission.copyrightStatement## http://creativecommons.org/licenses/by-nc/4.0 2018-12-13 2018-12-13 9 2 135 138 10.20454/jast.2018.1492