Research Article
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I-cluster points of filters

Year 2017, Volume: 5 Issue: 4, 195 - 202, 01.10.2017
https://izlik.org/JA65AT92MM

Abstract

In this paper, we have introduced the concept of cluster point of a filter on a topological space and studied its various properties. We have proved the necessary condition for a filter to have an cluster point. Most of the work in this paper is inspired from [2] and .

References

  • V. Bal J. erveansk P. Kostyrko, T. alt, convergence and continuity of real functions, Faculty of Natural Sciences, Constantine the Philosoper University, Nitra, Acta Mathematical 5, 43-50, 2002.
  • N. Bourbaki, General Topology, Part (I) (transl.), Addison- Wesley, Reading (1966).
  • K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), 165-172.
  • H. Fast, sur la convergence statistique, colloq. Math. 2 (1951), 241-244.
  • H. Halberstem, K. F. Roth, Sequences, Springer, New York, 1993.
  • D. S. Jamwal, R. Jamwal, S. Sharma, Convergence of filters, New Trends in Mathematical Sciences, 4, No. 4, (2016), 322-328.
  • R. Jamwal, S. Sharma and D. S. Jamwal, Some more results on Convergence of filters, New Trends in Mathematical Sciences, 5, No. 1, (2017), 190-195.
  • P. Kostyrko, T.alt, W. Wilczynski, convergence, Real Analysis, Exch. 26 (2) (2000/2001), 669-685.
  • P. Kostyrko, M. Maaj, T.alt, M. Sleziak, convergence and extremal limit points, Math. Slovaca, 55 (4) (2005), 443-464.
  • B. K. Lahiri, P. Das, Further results on limit superior and limit inferior, Math. Commun., 8 (2003), 151-156.
  • B. K. Lahiri, P. Das, and convergence in topological spaces, Math. Bohemica, 130 (2) (2005), 153-160.
  • B. K. Lahiri, P. Das, and convergence of nets, Real Analysis Exchange, 33 (2) (2007/2008), 431-442.
  • M. Maaj, T.alt, Statistical convergence of subsequences of a given sequence, Math. Bohemica, 126 (2001), 191-208.
  • M. Mursaleen and A. Alotaibi, On I–convergence in random 2–normed spaces, Math. Slovaca, 61(6) (2011) 933–940.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010) 359-371.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62(1) (2012) 49-62.
  • M. Mursaleen, S. A. Mohiuddine and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010) 603-611.
  • I. Niven, H. S. Zuckerman, An introduction to the theory of numbers, 4th Ed., John Wiley, New York, 1980.
  • T.alt, On statistically convergent sequences of real numbers, Mathematical Slovaca, 30 (1980), No. 2, 139-150.
  • T.alt, B. C. Tripathy, M. Ziman, On convergence field, Italian J. of Pure Appl. Math. 17 (2005), 45-54.
  • A.Sahiner, M. Gürdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5) (2007), 1477-1484.
  • I. J. Schoenberg, The integrability of certain function and related summability methods, Am. Math. Mon. 66 (1959), 361-375.
  • S. Willard, General Topology, Addison-Wesley Pub. Co. 1970.

Year 2017, Volume: 5 Issue: 4, 195 - 202, 01.10.2017
https://izlik.org/JA65AT92MM

Abstract

References

  • V. Bal J. erveansk P. Kostyrko, T. alt, convergence and continuity of real functions, Faculty of Natural Sciences, Constantine the Philosoper University, Nitra, Acta Mathematical 5, 43-50, 2002.
  • N. Bourbaki, General Topology, Part (I) (transl.), Addison- Wesley, Reading (1966).
  • K. Demirci, I-limit superior and limit inferior, Math. Commun. 6 (2001), 165-172.
  • H. Fast, sur la convergence statistique, colloq. Math. 2 (1951), 241-244.
  • H. Halberstem, K. F. Roth, Sequences, Springer, New York, 1993.
  • D. S. Jamwal, R. Jamwal, S. Sharma, Convergence of filters, New Trends in Mathematical Sciences, 4, No. 4, (2016), 322-328.
  • R. Jamwal, S. Sharma and D. S. Jamwal, Some more results on Convergence of filters, New Trends in Mathematical Sciences, 5, No. 1, (2017), 190-195.
  • P. Kostyrko, T.alt, W. Wilczynski, convergence, Real Analysis, Exch. 26 (2) (2000/2001), 669-685.
  • P. Kostyrko, M. Maaj, T.alt, M. Sleziak, convergence and extremal limit points, Math. Slovaca, 55 (4) (2005), 443-464.
  • B. K. Lahiri, P. Das, Further results on limit superior and limit inferior, Math. Commun., 8 (2003), 151-156.
  • B. K. Lahiri, P. Das, and convergence in topological spaces, Math. Bohemica, 130 (2) (2005), 153-160.
  • B. K. Lahiri, P. Das, and convergence of nets, Real Analysis Exchange, 33 (2) (2007/2008), 431-442.
  • M. Maaj, T.alt, Statistical convergence of subsequences of a given sequence, Math. Bohemica, 126 (2001), 191-208.
  • M. Mursaleen and A. Alotaibi, On I–convergence in random 2–normed spaces, Math. Slovaca, 61(6) (2011) 933–940.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports, 12(62)(4) (2010) 359-371.
  • M. Mursaleen and S. A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca, 62(1) (2012) 49-62.
  • M. Mursaleen, S. A. Mohiuddine and O. H. H. Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl., 59 (2010) 603-611.
  • I. Niven, H. S. Zuckerman, An introduction to the theory of numbers, 4th Ed., John Wiley, New York, 1980.
  • T.alt, On statistically convergent sequences of real numbers, Mathematical Slovaca, 30 (1980), No. 2, 139-150.
  • T.alt, B. C. Tripathy, M. Ziman, On convergence field, Italian J. of Pure Appl. Math. 17 (2005), 45-54.
  • A.Sahiner, M. Gürdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math., 11(5) (2007), 1477-1484.
  • I. J. Schoenberg, The integrability of certain function and related summability methods, Am. Math. Mon. 66 (1959), 361-375.
  • S. Willard, General Topology, Addison-Wesley Pub. Co. 1970.
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Rohini Jamwal, This is me

Renu Renu This is me

Dalip Singh Jamwal This is me

Publication Date October 1, 2017
IZ https://izlik.org/JA65AT92MM
Published in Issue Year 2017 Volume: 5 Issue: 4

Cite

APA Jamwal,, R., Renu, R., & Jamwal, D. S. (2017). I-cluster points of filters. New Trends in Mathematical Sciences, 5(4), 195-202. https://izlik.org/JA65AT92MM
AMA 1.Jamwal, R, Renu R, Jamwal DS. I-cluster points of filters. New Trends in Mathematical Sciences. 2017;5(4):195-202. https://izlik.org/JA65AT92MM
Chicago Jamwal, Rohini, Renu Renu, and Dalip Singh Jamwal. 2017. “I-Cluster Points of Filters”. New Trends in Mathematical Sciences 5 (4): 195-202. https://izlik.org/JA65AT92MM.
EndNote Jamwal, R, Renu R, Jamwal DS (October 1, 2017) I-cluster points of filters. New Trends in Mathematical Sciences 5 4 195–202.
IEEE [1]R. Jamwal, R. Renu, and D. S. Jamwal, “I-cluster points of filters”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 195–202, Oct. 2017, [Online]. Available: https://izlik.org/JA65AT92MM
ISNAD Jamwal,, Rohini - Renu, Renu - Jamwal, Dalip Singh. “I-Cluster Points of Filters”. New Trends in Mathematical Sciences 5/4 (October 1, 2017): 195-202. https://izlik.org/JA65AT92MM.
JAMA 1.Jamwal, R, Renu R, Jamwal DS. I-cluster points of filters. New Trends in Mathematical Sciences. 2017;5:195–202.
MLA Jamwal, Rohini, et al. “I-Cluster Points of Filters”. New Trends in Mathematical Sciences, vol. 5, no. 4, Oct. 2017, pp. 195-02, https://izlik.org/JA65AT92MM.
Vancouver 1.Rohini Jamwal, Renu Renu, Dalip Singh Jamwal. I-cluster points of filters. New Trends in Mathematical Sciences [Internet]. 2017 Oct. 1;5(4):195-202. Available from: https://izlik.org/JA65AT92MM