Prof. BRIJKISHORE TYAGI

Prof. Brij Kishore Tyagi (Prof. B. K. Tyagi)
QUALIFICATIONS :- M.Sc., M.Phil., Ph.D.
SUBJECT :- MATHEMATICS
AREAS OF INTEREST :- TOPOLOGY / DATBASES
Topology is an area of pure mathematics which is
fundamental to all mathematics. Particularly we work in point set topology and
in topological groups. These are the classical areas of topology.
? Teaching Experience :- Taught B.Sc. (Hons.)/ M.Sc. / B.Tech Mathematics
Papers.
? Research Guidance/ Supervision
Ph.D. Scholars: The followiing students have completed their Ph.D. under my guidance.
1. Rabindra Nath Dutta (Degree Awarded, 2010 ) from Jamia Millia Islamia.
2. Harsh V. S. Chauhan (Degree Awarded, 2019) from University of Delhi.
3. Sumit Singh (Degree Awarded, 2021) from University of Delhi.
4. Manoj Bhardwaj (Degree Awarded, 2021) from University of Delhi.
5. Sheetal Luthra (Degree Awarded, 2022) from University of Delhi.
6. Gaurav Kumar (Degree Awarded, 2024) from University of Delhi.
7. Sumit (Degree awarded ,2025) from University of Delhi).
8. Vikesh (Degree awarded ,2025) from University of Delhi).

Ph.D. Scholar under Supervision:
? One Ph.D. student is currently working under my guidance from
the Department of Mathematics, University of Delhi (In joint supervision).
M.Phil. Guidance: - Seven M.Phil. Degrees are guided

? INVITED RESOURCE PERSON/ TALK IN CONFERENCE

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? Lecture as a resource person on “Logical Problems” in a FDP
held at Jamia Millia Islamia, 26 Nov., 1998.
? Invited lecture on “Logical Paradoxes” in a conference, held at
Bundelkhand University, 4 April, 2000.
? Lecture as a resource person on “Fuzzy databases” in a FDP,
held at Jawaharlal Nehru University, 10 Nov., 2008.

Professor in Mathematics

Institution: ATMARAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI, DELHI

Total Teaching Experience: 32 years

REAL ANALYSIS, COMPLEX ANALYSIS, MODERN ALGEBRA, THEORY OF COMPUTATIONS, SCIENTIFIC COMPUTING, ENGINEERING MATHEMATICS

List of Published Research Papers/ Book:
? B. K. Tyagi, First Course in Metric Spaces, (Foundation Book).
1. Naseem, B. K. Tyagi, Regular fuzzy spaces and fuzzy almost regular spaces, Mat.
Vesnik 40 (1988), no. 2, 97–108.
2. A. Naseem,   B. K. Tyagi, A characterization of regular fuzzy spaces, Mat. Vesnik 41 (1989), no. 2,
65–70.
3. A. Naseem,   B. K. Tyagi, On fuzzy almost continuous functions, Fuzzy Sets and
Systems 41 (1991), no. 2, 221–232.
4. P. C. Saxena,  B. K. Tyagi, Fuzzy functional dependencies and independencies in extended fuzzy
relational database models, Fuzzy Sets and Systems 69 (1995), no. 1, 65–89.
5. B. K. Tyagi,  Sharfuddin, A. Dutta, R. N. Tayal, D. Kumar, .A complete axiomatization of fuzzy
functional dependencies using fuzzy function, Fuzzy Sets and Systems 151 (2005), no. 2,
363–379.
6. J. K. Kohli,   D. Singh,  B. K. Tyagi, Quasi locally connected spaces and pseudo locally connected
spaces, Comment. Math. 50 (2010), no. 2, 183–199.
7. J. K. Kohli, D. Singh,   B. K. Tyagi, Quasi perfectly continuous functions and their function spaces,
Sci. Stud. Res. Ser. Math. Inform. 21 (2011), no. 2, 23–40.
8. B. K. Tyagi,  J. K. Kohli,   D. Singh, Rcl-supercontinuous functions, Demonstratio Math. 46 (2013),
no. 1, 229–244.
9. J. K. Kohli,   D. Singh,   B. K. Tyagi, Between local connectedness and sum connectedness,
Comment. Math. 53 (2013), no. 1, 3–16.
10. J. K. Kohli,  B. K. Tyagi , D. Singh,  J. Aggarwal, Rδ-supercontinuous functions, Demonstr.
Math. 47 (2014), no. 2, 433–448.
11. D. Singh B. K. Tyagi, J. Aggarwal, J. K.  Kohli, Rz-supercontinuous functions, Math.
Bohem. 140 (2015), no. 3, 329–343.
12. B. K. Tyagi,   H. V. S. Chauhan, R. Choudhary, On γθ-operator and θ-connected sets in
generalized topological spaces, J. Adv. Stud. Topol. 6 (2015), no. 4, 135–142.
13. B. K. Tyagi, H. V. S. Chauhan, A remark on extremally μ-disconnected generalized topological
spaces, Math. Appl. (Brno) 5 (2016), no. 1, 83–90.
14.  J. K Kohli, D. Singh, B. K.  Tyagi, Rcl-locally connected spaces, Sci. Stud. Res. Ser. Math.
Inform. 26 (2016), no. 1, 25–38.
15. B. K. Tyagi, H. V. S. Chauhan, On generalized closed sets in generalized topological spaces,
Cubo 18 (2016), no. 1, 27–45.
16. B. K. Tyagi,  S. Singh, M. Bhardwaj, Pβ-connectedness in topological spaces, Demonstr.
Math. 50 (2017), no. 1, 299–308.
17. B. K. Tyagi, H. V. S.  Chauhan, On some separation axioms in generalized topological spaces,
Questions Answers Gen. Topology 36 (2018), no. 1, 9–29.
18. B. K. Tyagi, H. V. S. Chauhan, cμ-cμ-connectedness and V-θ-connectedness in generalized
topological spaces, An. Univ. Oradea Fasc. Mat. 25 (2018), no. 2, 99–106.
19. B. K. Tyagi, M.  Bhardwaj,  S. Singh, Hyperconnectedness modulo an ideal, Filomat 32 (2018),
no. 18, 6375–6386.

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20. B. K. Tyagi, M. Bhardwaj, S. Singh, αβ-connectedness as a characterization of connectedness, J.
Adv. Stud. Topol. 9 (2018), no. 2, 119–129.
21. B. K. Tyagi,  S. Luthra, H. V. S.  Chauhan On new types of sets via γ-open sets in (a) topological
spaces, Cubo 20 (2018), no. 2, 41–52.
22. B. K. Tyagi, M. Bhardwaj, S. Singh, Cl∗-connectedness and Cl−Cl∗-connectedness in ideal
topological spaces, Mat. Bilten 42 (2018), no. 2, 91–100.
23. B. K.Tyagi,  S. Singh, M. Bhardwaj,  Chauhan, Harsh V. S., Some strong forms of connectedness
in topological spaces, J. Adv. Stud. Topol. 10 (2019), no. 1, 20–27.
24. B. K. Tyagi, S. Singh,   M. Bhardwaj, bβ-connectedness as a simultaneous characterization of β-
connectedness, γ-connectedness and ββ-connectedness, Questions Answers Gen.
Topology 37 (2019), no. 2, 135–153.
25. B. K. Tyagi, M. Bhardwaj, S. Sumit, Sα-connectedness in topological spaces, Jordan J. Math.
Stat. 12 (2019), no. 3, 409–424.
26. B. K. Tyagi, S. Singh M. Bhardwaj , Ideal analogues of some variants of the Hurewicz property,
Filomat 33 (2019), no. 9, 2725–2734.
27. B. K.Tyagi, H. V. S. Chauhan, On semi-open sets and feebly open sets in generalized topological
spaces, Proyecciones 38 (2019), no. 5, 875–896.
28. S. Sumit,   B. K. Tyagi,   M. Bhardwaj, An ideal version of the star-C-Hurewicz covering property,
Filomat 33 (2019), no. 19, 6385–6393.
29. B. K. Tyagi, S. Singh, M. Bhardwaj, Almost contra-PS-continuity in topological spaces, Ann. Univ.
Sci. Budapest. Eötvös Sect. Math. 62 (2019), 61–78.
30. M.  Bhardwaj, B. K.  Tyagi.  S. Singh, Relativization of star-C-Hurewicz property in topological
spaces, Bull. Iranian Math. Soc. 46 (2020), no. 4, 1101–1115.
31. B. K. Tyagi, S.  Sumit, M.  Bhardwaj ,  Independent form of (θ,s)-continuous functions in topological
spaces, Proyecciones 39 (2020), no. 3, 495–515.
32. S. Luthra,  B. K. Tyagi, Homeomorphisms between function spaces, J. Adv. Stud. Topol. 11 (2020),
no. 1-2, 1–5.
33. S. Singh, B. K. Tyagi,  M. Bhardwaj, The absolutely strongly star-Hurewicz property with respect to
an ideal, Tatra Mt. Math. Publ. 76 (2020), 81–94.
34. S. Luthra, H. V. S. Chauhan, B.K. Tyagi, Quasi-N-open sets in (a)topological spaces, Jordan J.
Math. Stat. 13 (2020), no. 4, 505–517.
35. S. Singh, B. K. Tyagi, M. Bhardwaj, Pre-Hurewicz and related spaces, Questions Answers Gen.
Topology 38 (2020), no. 1, 71–85.
36. S. Singh, B. K. Tyagi, Remarks on almost Menger and weakly Menger spaces, Questions Answers
Gen. Topology 38 (2020), no. 2, 127–131.
37. M. Bhardwaj,   B. K. Tyagi, S. Singh, On SIH property and SSIH property in topological spaces,
Khayyam J. Math. 7 (2021), no. 1, 65–76.
38. M. Bhardwaj, B. K. Tyagi, S. Singh, Star-Hurewicz modulo an ideal property in topological spaces,
J. Indian Math. Soc. (N.S.) 88 (2021), no. 1-2, 33–45.
39. S. Singh,   B. K. Tyagi,  M. Bhardwaj, Sequence selection properties in Cp(X) with the double
ideals, Math. Slovaca 71 (2021), no. 1, 147–154.
40. B. K. Tyagi,  S. Singh, M. Bhardwaj, Covering properties defined by preopen sets, Asian-Eur. J.
Math. 14 (2021), no. 3, Paper No. 2150035, 15 pp.
41. M. Bhardwaj,  S. Singh, B.K. Tyagi, .Relative version of star-Hurewicz property, Acta Math.
Hungar. 164 (2021), no. 1, 85–100.

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42. G. Kumar, B. K.  Tyagi, Weakly strongly star-Menger spaces, Cubo 23 (2021), no. 2, 287–298.
43. S. Luthra, H. V. S. Chauhan, B. K. Tyagi, Selective separability in (a)topological spaces,
Filomat 35 (2021), no. 11, 3745–3758.
44. S. Singh, B. K.Tyagi, M. Bhardwaj, The almost I-Hurewicz covering property, Filomat 35 (2021),
no. 14, 4777–4787.
45. B. K. Tyagi, M. Bhardwaj, S. Singh, Some strong forms of connectedness in topological spaces,
Questions Answers Gen. Topology 39 (2021), no. 1, 5–26.
46. B. K. Tyagi, M.  Bhardwaj, S.  Singh, Some characterizations of connectedness in topological
spaces, Questions Answers Gen. Topology 39 (2021), no. 2, 103–125.
47. S. Mittal, B. K. Tyagi, Characterizations of countably ρI-compact ideal topological spaces, Sci.
Stud. Res. Ser. Math. Inform. 31 (2021), no. 1, 141–150.
48. B. K. Tyagi, S. Luthra, Open-point and bi-point open topologies on continuous functions between
topological (spaces) groups, Mat. Vesnik 74 (2022), no. 1, 56–70.
49. S. Luthra, H. V. S. Chauhan,  B. K. Tyagi, T., Cemil, Covering properties by (a)-θ-open sets
in (a)topological spaces, Palest. J. Math. 11 (2022), no. 2, 531–541.
50. M. Kumar, B. K. Tyagi, Cardinal invariants and special maps of quasicontinuous functions with the
topology of pointwise convergence, Appl. Gen. Topol. 23 (2022), no. 2, 303–314.
51. S. Luthra, H. V. S. Chauhan, B. K. Tyagi, Selective version of star-semi-Lindelöfness
in (a)topological spaces, Tatra Mt. Math. Publ. 81 (2022), 39–56.
52. G. Kumar, B. K. Tyagi, Remarks on semi-Menger and star semi-Menger spaces, Tatra Mt. Math.
Publ. 81 (2022), 57–68.
53. S. Luthra, H. V. S. Chauhan, B. K. Tyagi, Covering properties by (a)-semi-open sets
in (a)topological spaces, Missouri J. Math. Sci. 34 (2022), no. 2, 146–167.
54. S. Mittal, G. Kumar, B. K. Tyagi, On some set properties, Filomat 36 (2022), no. 19, 6473–6479.
55. S. Luthra, B. K. Tyagi, Some remarks on uniform convergence topology, Questions Answers Gen.
Topology 40 (2022), no. 1, 43–52.
56. S. Luthra, H. V. S.  Chauhan, B. K.  Tyagi, The bi-clp-compact-open topology on function spaces,
Questions Answers Gen. Topology 40 (2022), no. 2, 113–123.
57. V. Kumar, B. K.  Tyagi, Subgroups of products of para τ-discrete semitopological groups,
Filomat 37 (2023), no. 7, 2165–2172.
58. G. Kumar, B. K. Tyagi, On variants of θ-Menger spaces, Filomat 37 (2023), no. 15, 5075–5085.
59. G. Kumar, B. K. Tyagi, S.  Mittal, Some variants of the Rothberger property using generalized open
sets, Southeast Asian Bull. Math. 47 (2023), no. 4, 479–494.
60. V. Kumar, B. K. Tyagi, On ωs-balanced semitopological groups, Quaest. Math. 46 (2023), no. 12,
2577–2591.
61. S. Mittal, G. Kumar, B. K. Tyagi, Relative versions of star-Menger property, Math.
Slovaca 74 (2024), no. 4, 1001–1010.
62. V. Kumar, B. K. Tyagi, Projectively regular (T2,T1) weakly developable semitopological groups,
Topology Appl. 356 (2024), Paper No. 109028, 12 pp.

BOOK

TITLE: " First Course in METRIC SPACES"

PUBLISHER: FOUNDATION BOOKS CAMBRIDGE UNIVERSITY PRESS INDIA PVT LIMITED

YEAR OF PUBLICATION: 2010

FDP  : Conducted one week Faculty Development Programme at Department of Applied mathematics DTU from 1-12-2025 to 5-12- 2025

TITLE:" Recent Trends in Mathematics and its Applications for Sustainable Developments"

Coordinator: Brijkishore Tyagi

Co-coordinator; Dhirendra Kumar and Anshul Arora