-convergence and extremal -limit points

Pavel Kostyrko; Martin Máčaj; Tibor Šalát; Martin Sleziak

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 4, page 443-464
  • ISSN: 0139-9918

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Kostyrko, Pavel, et al. "$\mathcal {I}$-convergence and extremal $\mathcal {I}$-limit points." Mathematica Slovaca 55.4 (2005): 443-464. <http://eudml.org/doc/32332>.

@article{Kostyrko2005,
author = {Kostyrko, Pavel, Máčaj, Martin, Šalát, Tibor, Sleziak, Martin},
journal = {Mathematica Slovaca},
keywords = {density of sets; ideal of sets; porosity; - and -convergence; ; , , maximal ideal},
language = {eng},
number = {4},
pages = {443-464},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {$\mathcal \{I\}$-convergence and extremal $\mathcal \{I\}$-limit points},
url = {http://eudml.org/doc/32332},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Kostyrko, Pavel
AU - Máčaj, Martin
AU - Šalát, Tibor
AU - Sleziak, Martin
TI - $\mathcal {I}$-convergence and extremal $\mathcal {I}$-limit points
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 4
SP - 443
EP - 464
LA - eng
KW - density of sets; ideal of sets; porosity; - and -convergence; ; , , maximal ideal
UR - http://eudml.org/doc/32332
ER -

References

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  1. ALEXANDER R., Density and multiplicative structure of sets of integers, Acta Arith. 12 (1967), 321-332. (1967) MR0211979
  2. BACHRATÁ K., The maximal ideals of C ( 0 , 1 ) , Práce a Štúdie V.Š. Dopravу a Spojov v Žiline, Sér. Mat.-Fуz. 8 (1992), 5-7. (1992) MR1291582
  3. BROWN Т. С.-FREEDMAN A. R., The uniform density of sets of integers and Fermat's Last Theorem, С. R. Math. Acad. Sci. Soc. R. Сan. 12 (1990), 1-9. (1990) Zbl0701.11011
  4. BUСK R. С., The measure theoretic approach to density, Amer. J. Math. 68 (1946), 560 580. (1946) MR0018196
  5. BUСK R. С., Generalized asymptotic density, Amer. J. Math. 75 (1953), 335-346. (1953) MR0054000
  6. СARLSON S., Cauchy sequences and function rings, Amer. Math. Monthlу 88 (1981), 700-701. (1981) MR1539796
  7. ČERVEŇANSKÝ J., Statistical convergence and statistical continuity, Zb. Ved. Prác MtF SТU 6 (1998), 207-212. (1998) 
  8. СONNOR J. S., The statistical and strong p-Cesàro convergence of sequences, Analуsis (Munich) 8 (1988), 47-63. (1988) MR0954458
  9. СONNOR J. S., Two valued measures and summability, Analуsis (Munich) 10 (1990), 373-385. (1990) MR1085803
  10. СONNOR J. S.-KLINE J., On statistical limit points and the consistency of statistical convergence, J. Math. Anal. Appl. 197 (1996), 392-399. (197) MR1372186
  11. FASТ H., Sur la convergence statistique, Соllоq. Math. 2 (1951), 241-244. (1951) MR0048548
  12. FREEDMAN A. R.-SEMBER J. J., Densities and summability, Pacific J. Math. 95 (1981), 293-305. (1981) Zbl0504.40002MR0632187
  13. FRIDY J. A., On statistical convergence, Analуsis (Munich) 5 (1985), 301-313. (1985) Zbl0588.40001
  14. FRIDY J. A., Statistical limit points, Prоc. Amer. Math. Sоc. 118 (1993), 1187-1192. (1993) Zbl0776.40001MR1181163
  15. FRIDY J. A.-ORHAN, С, Statistical limit superior and limit inferior, Prоc. Amer. Math.Sоc. 125 (1997), 3625-3631. (1997) Zbl0883.40003MR1416085
  16. GILLMAN L.-JERISON M., Rings of Continuous Functions, Van Nоstrand, Princetоn, 1950. (1950) MR0116199
  17. KOSТYRKO P.-MAČAJ M.-ŠALÁТ Т.-SТRAUСH O., On statistical limit points, Prоc. Amer. Math. Sоc. 129 (2001), 2647-2654. 
  18. KOSТYRKO P.-ŠALÁТ Т.-WILСZYŃSKI W., -convergence, Real Anal. Exchange 26 (2000-2001), 669-686. 
  19. KURAТOWSKI С., Topologie I, PWN, Warszawa, 1958. (1958) 
  20. MAHARAM D., Finitely additive measures on the integers, Sankhуä Ser. A 38 (1976), 44-54. (1976) Zbl0383.60008MR0473132
  21. MAČAJ M.-MIŠÍK L.-ŠALÁТ Т.-ТOMANOVÁ J., On a class of densities of sets of positive integers, Acta Math. Univ. Соmenian. (N.S.) 72 (2003), 213-221. Zbl1087.11006MR2040266
  22. MAZUR K., F σ -ideals and and ω 1 ω 1 * -gaps in the Boolean algebras P ( ω ) / I , Fund. Math. 138 (1991), 103-111. (1991) MR1124539
  23. MIKUSIŃSKI P., Axiomatic theory of convergence, Pr. Nauk. Uniw. ŚI. Katow. 12 (1982), 13-21. (Polish) (1982) Zbl0508.40003MR0663359
  24. MILLER H. I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811-1819. (1995) Zbl0830.40002MR1260176
  25. NAGATA J., Modern General Topology, Noth-Holland Publ. Comp., Amsterdam-London, 1974. (1974) MR0474164
  26. NEUBRUN T.-SMÍTAL J.-ŠALÁT T., On the structure of the space M ( 0 , 1 ) , Rev. Roumaine Math. Pures Appl. 13 (1968), 377-386. (1968) MR0234275
  27. NURAY F.-RUCKLE W. H., Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513-527. Zbl0955.40001MR1758553
  28. OLEVSKII V., A note on the Banach-Steinhaus theorem, Real Anal. Exchange 17 (1991-1992), 399-401. (1991) MR1147379
  29. OSTMANN H. H., Additive Zahlentheorie I, Springer-Verlag, Berlin-Gottingen-Heidelberg, 1956. (1956) Zbl0072.03101MR0098721
  30. PETERSEN G. M., Regular Matrix Transformations, Mc Graw-Hill, London-New York-Toronto-Sydney, 1966. (1966) Zbl0159.35401MR0225045
  31. POWELL B. J.-ŠALÁT T., Convergene of subseries of the harmonic series and asymptotic densities of sets of positive integers, Publ. Inst. Math. (Beograd) (N.S.) 50(64) (1991), 60-70. (1991) MR1252159
  32. ŠALÁT T., On statistically convergent sequences of real numbers, Math. Slovaca 30 (1980), 139-150. (1980) Zbl0437.40003MR0587239
  33. ŠALÁT T.-TIJDEMAN R., Asymptotic densities of sets of positive integers, Math. Slovaca 33 (1983), 199-207. (1983) Zbl0516.10052MR0699090
  34. ŠALÁT T.-TIJDEMAN R., On density measures of sets of positive integers, In: Topics in Classical Number Theory. Colloq. Math. Soc. Janos Bolyai 34, Budapest, 1981, pp. 1445-1457. (1981) MR0781191
  35. ŠALÁT T.-TOMANOVA J., On the product of divisors of a positive integer, Math. Slovaca 52 (2002), 271-287. Zbl1005.11002MR1936333
  36. SCHINZEL A.-ŠALÁT T., Remarks on maximum and minimum exponents in factoring, Math. Slovaca 44 (1994), 505-514. (1994) Zbl0821.11004MR1338424
  37. SCHOENBERG I. J., The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375. (1959) Zbl0089.04002MR0104946
  38. THOMSON B. S., Real Functions, Springer-Verlag, Berlin-Gottingen-Heidelberg-New York-Tokyo, 1985. (1985) Zbl0581.26001MR0818744
  39. ZAJÍČEK L., Porosity and σ -porosity, Real Anal. Exchange 13 (1987-88), 314-350. (1987) Zbl0666.26003MR0943561

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