Journal of Advanced Studies in Topology <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> Reflexive retracts and its properties <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> C. R. Parvathy S. Bhuvaneshwari Copyright (c) 2019 Modern Science Publishers 2019-01-31 2019-01-31 10 1 1 7 10.20454/jast.2019.1494 A note on the lattice of L-topologies <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> Pinky . T.P Johnson Copyright (c) 2019 Modern Science Publishers 2019-02-03 2019-02-03 10 1 8 19 10.20454/jast.2019.1489 Some strong forms of connectedness in topological spaces <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> B. K. Tyagi Sumit Singh Manoj Bhardwaj Harsh V. S. Chauhan Copyright (c) 2019 Modern Science Publishers 2019-02-03 2019-02-03 10 1 20 27 10.20454/jast.2019.1497 Compact and extremally disconnected spaces via generalized continuous functions <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> Zeinab Bandpey Bhamini M. P. Nayar Copyright (c) 2019 Modern Science Publishers 2019-02-09 2019-02-09 10 1 28 34 10.20454/jast.2019.1507 Semi compactness in fuzzifying bitopological spaces <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> A. A. Allam A. M. Zahran A. K. Mousa H. M. Binshahnah Copyright (c) 2019 Modern Science Publishers 2019-03-30 2019-03-30 10 1 35 48 10.20454/jast.2019.1499 Binary Cech closure spaces using binary ideals and binary grills <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> Tresa Mary Chacko Susha D. Copyright (c) 2019 Modern Science Publishers 2019-04-17 2019-04-17 10 1 49 57 10.20454/jast.2019.1503 Different proofs of theorems of Michael and Worrell <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> Terrence A. Edwards James E. Joseph Bhamini M. P. Nayar Copyright (c) 2019 Modern Science Publishers 2019-06-11 2019-06-11 10 1 58 61 10.20454/jast.2019.1539 Product of generalized quasi-uniform spaces <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> Sugata Adhya A. Deb Ray Copyright (c) 2019 Modern Science Publishers 2019-06-13 2019-06-13 10 1 62 67 10.20454/jast.2019.1520