Journal of Advanced Studies in Topology 2019-06-13T11:15:54+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> Reflexive retracts and its properties 2019-04-04T23:59:08+00:00 C. R. Parvathy S. Bhuvaneshwari <p>In this paper, we have introduced the notion of reflexive retract. A few levels of retracts were achieved. The first level is obviously the retract in the sense of Borsuk, and the second level is reflexive homotopy and its properties.</p> 2019-01-31T11:09:59+00:00 Copyright (c) 2019 Modern Science Publishers A note on the lattice of L-topologies 2019-04-04T23:59:08+00:00 Pinky . T.P Johnson <p>In this paper, we study the lattice structure of the lattice \(F_{T,L}\) of all \(L\)-topologies determined by the families of Scott continuous functions for a given topological space \((X,T)\). Some properties are discussed for which the lattice \(F_{T,L}\) is complemented.</p> 2019-02-03T19:41:39+00:00 Copyright (c) 2019 Modern Science Publishers Some strong forms of connectedness in topological spaces 2019-04-04T23:59:08+00:00 B. K. Tyagi Sumit Singh Manoj Bhardwaj Harsh V. S. Chauhan <p>In this paper, we study new separations of sets called half separated, half \(\alpha\)-separated, half semi separated, half pre-separated, half \(\beta\)-separated sets and corresponding to these notions introduced half connected, half \(\alpha\)-connected, half semi-connected, half pre-connected, half \(\beta\)-connected topological spaces, respectively. These are stronger forms of connectedness, \(\alpha\)-connectedness, semi-connectedness, pre-connectedness, \(\beta\)-connectedness respectively. The properties of these notions follow the same pattern.</p> 2019-02-03T00:00:00+00:00 Copyright (c) 2019 Modern Science Publishers Compact and extremally disconnected spaces via generalized continuous functions 2019-04-04T23:59:07+00:00 Zeinab Bandpey Bhamini M. P. Nayar <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In [12], the class of compact and extremally dinconnected spaces were studied using several investigative tools such as filters, graphs, functions, multifuctions and subsets of the space. These different approaches of investigation produced significant charecterizations and properties of this important class of spaces. In [3] we introduced three forms of generalized continuous functions by studying the class of u-continuous functions of Joseph, Kwack and Nayar [9] using the concepts of an α-set of Njastad [13]. The generalized continuous forms introduced there are: αu-continuous, semi-αu-contnuous and strongly u-continuous functions. In the present study we investigate the class of compact and extremally disconnected spaces using these generalized continuous functions.</p> </div> </div> </div> 2019-02-09T17:57:50+00:00 Copyright (c) 2019 Modern Science Publishers Semi compactness in fuzzifying bitopological spaces 2019-04-04T23:59:07+00:00 A. A. Allam A. M. Zahran A. K. Mousa H. M. Binshahnah <p>In this paper, we dene semi open sets in the subspaces of fuzzifying bitopological spaces and study some properties of these sets. We introduce and study the concepts of semi-compactness in fuzzifying bitopological spaces. Also we give some properties of the semi-compactness in fuzzifying bitopological spaces.</p> 2019-03-30T18:14:26+00:00 Copyright (c) 2019 Modern Science Publishers Binary Cech closure spaces using binary ideals and binary grills 2019-04-17T13:36:03+00:00 Tresa Mary Chacko Susha D. <p>In this paper we introduce binary Cech closure operators obtained from binary ideals and binary grills.<br>Here we describe some properties of the binary topology obtained from both binary ideals and binary grills.<br>Also we present the concept of compactness in both binary ideals and binary grills.</p> 2019-04-17T13:36:03+00:00 Copyright (c) 2019 Modern Science Publishers Different proofs of theorems of Michael and Worrell 2019-06-11T11:02:30+00:00 Terrence A. Edwards James E. Joseph Bhamini M. P. Nayar <p>Different proofs of theorems of E. Michael and J. M. Worrell, that paracompactness and metacompactness are closed continuous invariants are presented here. A result due to Joseph and Kwack that all open sets in \(Y\) have the form \(g(V)-g(X-V)\), where \(V\) is open in \(X\), if \(g:X \to Y\) is continuous, closed and onto is used to give these proofs. Also a characterization that a space is paracompact (metacompact) if and only if every ultrafilter of type \(P\) (type \(M\)) converges [5], is used to give another proof of the invariance of paracompactness and metacompactness under continuous closed surgections.</p> 2019-06-11T10:47:41+00:00 Copyright (c) 2019 Modern Science Publishers Product of generalized quasi-uniform spaces 2019-06-13T11:15:54+00:00 Sugata Adhya A. Deb Ray <p>In this paper, we introduce product \(g\)-quasi uniformity and show that product \(g\)-quasi uniformity induces the generalized product topology. We also provide a necessary and sucient condition for a mapping into product \(g\)-quasi uniform space to be \(g\)-quasi uniformly continuous. Further, we establish the equivalence between completeness of product \(g\)-quasi uniform space and that of the component spaces.</p> 2019-06-13T11:15:54+00:00 Copyright (c) 2019 Modern Science Publishers