Journal of Advanced Studies in Topology 2018-12-14T21:58:57+00:00 A. Ghareeb Open Journal Systems <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> Soft almost \(\alpha\)-continuous mappings 2018-12-14T21:58:57+00:00 S. S. Thakur A. S. Rajput <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> 2018-08-10T09:13:31+00:00 ##submission.copyrightStatement## Weak and strong forms of fuzzy \(\alpha\)-open (closed) sets and its applications 2018-12-14T21:58:57+00:00 Hakeem A. Othman Alanod M. Sibih <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> 2018-08-10T00:00:00+00:00 ##submission.copyrightStatement## Separation axioms on function spaces defined on bitopological spaces 2018-12-14T21:58:56+00:00 N. E. Muturi J. M. Khalagai G. P. Pokhariyal <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> 2018-08-22T21:31:37+00:00 ##submission.copyrightStatement## \(\alpha_\beta\)-Connectedness as a characterization of connectedness 2018-12-14T21:58:56+00:00 B. K. Tyagi Manoj Bhardwaj Sumit Singh <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> 2018-09-25T18:10:44+00:00 ##submission.copyrightStatement## On irresolute topological rings 2018-12-14T21:58:56+00:00 Haval M. Mohammed Salih <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> 2018-10-26T06:31:36+00:00 ##submission.copyrightStatement## Pre-\((\omega)\)separation axioms 2018-12-14T21:58:56+00:00 Rupesh Tiwari <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> 2018-12-13T07:13:49+00:00 ##submission.copyrightStatement##