I and I * -convergence in topological spaces

Benoy Kumar Lahiri; Pratulananda Das

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 2, page 153-160
  • ISSN: 0862-7959

Abstract

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We extend the idea of I -convergence and I * -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.

How to cite

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Lahiri, Benoy Kumar, and Das, Pratulananda. "$I$ and $I^*$-convergence in topological spaces." Mathematica Bohemica 130.2 (2005): 153-160. <http://eudml.org/doc/249587>.

@article{Lahiri2005,
abstract = {We extend the idea of $I$-convergence and $I^*$-convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.},
author = {Lahiri, Benoy Kumar, Das, Pratulananda},
journal = {Mathematica Bohemica},
keywords = {$I$-convergence; $I^*$-convergence; condition (AP); $I$-limit point; $I$-cluster point; condition (AP); -limit point; -cluster point},
language = {eng},
number = {2},
pages = {153-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$I$ and $I^*$-convergence in topological spaces},
url = {http://eudml.org/doc/249587},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Lahiri, Benoy Kumar
AU - Das, Pratulananda
TI - $I$ and $I^*$-convergence in topological spaces
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 2
SP - 153
EP - 160
AB - We extend the idea of $I$-convergence and $I^*$-convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.
LA - eng
KW - $I$-convergence; $I^*$-convergence; condition (AP); $I$-limit point; $I$-cluster point; condition (AP); -limit point; -cluster point
UR - http://eudml.org/doc/249587
ER -

References

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  2. 10.1524/anly.1988.8.12.47, Analysis 8 (1988), 47–63. (1988) Zbl0653.40001MR0954458DOI10.1524/anly.1988.8.12.47
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  4. 10.4064/cm-2-3-4-241-244, Colloq. Math. 2 (1951), 241–244. (1951) Zbl0044.33605MR0048548DOI10.4064/cm-2-3-4-241-244
  5. Sequences, Springer, New York, 1993. (1993) 
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  8. Topologie I, PWN, Warszawa, 1962. (1962) 
  9. Further results on I -limit superior and I -limit inferior, Math. Commun. 8 (2003), 151–156. (2003) MR2026393
  10. Statistical convergence of subsequences of a given sequence, Math. Bohem. 126 (2001), 191–208. (2001) MR1826482
  11. An introduction to the theory of numbers, 4th ed., John Wiley, New York, 1980. (1980) MR0572268
  12. On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139–150. (1980) MR0587239
  13. A note on I -convergence field, (to appear). (to appear) MR2203460
  14. 10.2307/2308747, Am. Math. Mon. 66 (1959), 361–375. (1959) MR0104946DOI10.2307/2308747

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