I-Dizisel Hausdorff Uzaylar

Year 2019, , 628 - 632, 15.10.2019

Hürmet Fulya Akız

https://doi.org/10.17714/gumusfenbil.548506

Abstract

Bu çalışmada öncelikle I-dizisel sürekli, I-dizisel
açık ve I-dizisel kapalı fonksiyonlar
tanıtılmıştır. Daha sonra, Hausdorff  uzaylardan
daha geniş bir yapı olan I-dizisel
Hausdorff uzayların tanımı ve bazı özellikleri verilmiştir.

Keywords

Hausdorff uzaylar, I-dizisel açık küme, I-dizisel kapalı küme

I-Sequentially Hausdorff Spaces

Abstract

In this study, we
first introduce the notions of  I-sequentially
continuous, I-sequentially open  and
I-sequentially closed functions. We also give the definition and some
properties of a I-sequentially Hausdorff space, which is a wider structure than
a Hausdorff space.

Keywords

Hausdorff spaces, I-sequentially open set, I-sequentially closed set

References

• Akız, H. F. ve Koçak, L., 2019. Sequentially Hausdorff and Full Sequentially Hausdorff Spaces, Commun. Fac. Sci. Univ. Ank. Series A1, 68 (2), 1724-1732.
• Banerjee, A. K. ve Banerjee, A., 2015. A Note On I-Convergence and I*-Convergence of Sequences and Nets In Topological Spaces, Matematicki Vesnik, 67(3), 212-221.
• Çakallı, H., 2011. On G-continuity, Comput. Math. Appl., 61, 313-318.
• Çakallı, H., 2012. Sequential definitions of connectedness, Appl. Math. Lett., 25, 461-465.
• Çakallı, H. ve Mucuk, O., 2013. On connectedness via a sequential method, Revista de la Union Matematica Argentina, 54 (2), 101-109.
• Fast, H., 1951. Sur la convegence statistique, Collog. Math. 2, 241-244.
• Halberstem, H. ve Roth, K. F., 1993. Sequences, Springer, New York.
• Kostyrko, P., Šalát, T. ve Wilczynski, W., 2001. I-convergence, Real Analysis Exch. 26 (2), 669–686.
• Kostyrko, P., Mačaj, M., Šalát, T. ve Sleziak, M., 2005. I-convergence and a extermal I-limit points, Math. Slovaca, 55 (4),443-464.
• Lahiri, B. K. ve Das, P., 2005. I and I*-convergence in topological spaces, Math. Bohemica, 130 (2), 153–160.
• Mucuk O., 2010. Topoloji ve Kategori, Nobel Yayınları, Ankara.
• Mucuk O. ve Şahan T., 2014. On G-Sequential Continuity, Filomat, vol.28, 1181-1189.
• Niven, I. ve Zuckerman, H. S., 1980. An introduction to the theory of numbers. 4th Ed., John Wiley, New York.
• Pal, S. K., 2014. I-Sequential Topological Spaces, Applied Mathematics E-notes, 14, 236-241.
• Schoenberg, I. J., 1959. The integrability of certain function and related summability methods. Am. Math. Mon. 66, 361–375.