Bol. Soc. Paran. Mat. (3s.) v. 36 2 (2018): 17–31. c SPM –ISSN-2175-1188 on line ISSN-00378712 in press SPM: www.spm.uem.br/bspm doi:10.5269/bspm.v36i2.29377 p-I-Generator And p 1 -I-Generator In Bitopology S. Acharjee and B. C. Tripathy abstract: In this article, we investigate several relations between p-I-generator, p 1 -I-generator with p-Lindel¨ of and p 1 -Lindel¨ of spaces by using τ i -codense, (i, j )- meager set, (i, j )-nowhere dense set and perfect mapping of bitopological space. Various relations between p-compactness, p-Lindel¨ ofness, p 1 -Lindel¨ ofness, topolog- ical ideal, (i, j )-meager, (i, j )-Baire space in bitopological space are investigated. Some properties are studied by using perfect mapping in a product bitopological space. It is found that bitopological space has many applications in real life. Key Words: opological ideal, p-Lindel¨of, p 1 -Lindel¨of, pairwise weakly Lin- del¨of, pairwise almost Lindel¨ of. Contents 1 Introduction, motivation and scopes of bitopological space in other areas of mathematics and natural science. 17 2 Some preliminary definitions 20 3 Main results 22 4 Relations of p-I-generator and p 1 -I-generator with perfect mapping 25 5 On product bitopology 27 6 Conclusion 28 1. Introduction, motivation and scopes of bitopological space in other areas of mathematics and natural science. Kelly [1] introduced bitopological space via quasi-pseudo metric and systemati- cally investigated its various important properties. It has drawn direct and indirect attentions of many point set topologists, fuzzy topologists, engineers, researchers of medical science, computer scientists, economists etc. for its applications in their respective areas. Definition of topological ideal is well known. Topological ideal I and σ-ideal can be found in Dontchev et al.[2]. Ideal of all nowhere dense sets and ideal of all 2010 Mathematics Subject Classification: 54E55. Submitted October 05, 2015. Published April 18, 2016 17 Typeset by B S P M style. c  Soc. Paran. de Mat.