Statistical convergence in topology

We introduce and investigate statistical convergence in topological and uniform spaces and show how this convergence can be applied to selection principles theory, function spaces and hyperspaces.

[1]  M. K. Khan,et al.  Tauberian theorems via statistical convergence , 1998 .

[2]  Manuel Sanchis,et al.  Ultrafilter-limit points in metric dynamical systems , 2007 .

[3]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[4]  A. V. Arkhangel’skiǐ Topological Function Spaces , 1991 .

[5]  J. S. Connor,et al.  THE STATISTICAL AND STRONG p-CESARO CONVERGENCE OF SEQUENCES , 1988 .

[6]  L. Kočinac Some covering properties in topological and uniform spaces , 2006 .

[7]  J. Connor $R$-type summability methods, Cauchy criteria, $P$-sets and statistical convergence , 1992 .

[8]  Sur Les Densités de Certaines Suites D'Entiers , 1989 .

[9]  A. D. Gadjiev,et al.  Some approximation theorems via statistical convergence , 2002 .

[10]  G. Maio,et al.  Some covering properties of hyperspaces , 2008 .

[11]  Marion Scheepers,et al.  The Combinatorics of Open Covers , 1996 .

[12]  Pratulananda Das,et al.  $I$ and $I^*$-convergence in topological spaces , 2005 .

[13]  H. Fast,et al.  Sur la convergence statistique , 1951 .

[14]  P. Heywood Trigonometric Series , 1968, Nature.

[15]  B. Tsaban Some New Directions in Infinite-combinatorial Topology , 2004, math/0409069.

[16]  E. T. An Introduction to the Theory of Numbers , 1946, Nature.

[17]  J. A. Fridy,et al.  ON STATISTICAL CONVERGENCE , 1985 .

[18]  L. Kočinac Selection principles and covering properties in topology , 2006 .

[19]  M. Scheepers,et al.  Combinatorics of open covers (VIII) , 2004 .

[20]  M. Scheepers,et al.  Combinatorics of open covers (VII): Groupability , 2003 .

[21]  Tibor Šalát,et al.  On statistically convergent sequences of real numbers , 1980 .

[22]  M. Scheepers Combinatorics of open covers I: Ramsey theory , 1996 .

[23]  I. J. Schoenberg The Integrability of Certain Functions and Related Summability Methods , 1959 .

[24]  W. Hurewicz Über eine Verallgemeinerung des Borelschen Theorems , 1926 .

[25]  S. Naimpally,et al.  Uniformizing (proximal) Δ-topologies , 2004 .

[26]  O. Strauch,et al.  ON STATISTICAL LIMIT POINTS , 2000 .

[27]  H. I. Miller,et al.  A measure theoretical subsequence characterization of statistical convergence , 1995 .

[28]  L. Kočinac Selection principles in uniform spaces , 2003 .

[29]  Allen R. Freedman,et al.  Densities and summability. , 1981 .

[30]  Serpil Pehlivan,et al.  Statistical cluster points and turnpike , 2000 .

[31]  L. Kočinac Closure properties of function spaces , 2003 .

[32]  T. Nogura,et al.  CONVERGENCE PROPERTIES OF HYPERSPACES , 2007 .