Research Article
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Year 2023, Volume: 5 Issue: 2, 41 - 46, 30.11.2023

Osman Mucuk Mina Betül Teke

https://doi.org/10.47087/mjm.1301293

Abstract

References

  • A. Açıkgöz, H. Çakallı, F. Esenbel and LDR Kocinac, A quest of G-continuity in neutrosophic spaces, Mathematical Methods in the Applied Sciences, 44 (9) (2021) 7834-7844.
  • J. Antoni, On the A-continuity of real functions II, Math. Slovaca, 36, No.3 (1986) 283-287.
  • J. Antoni, T. Salat, On the A-continuity of real functions, Acta Math. Univ. Comenian, 39 (1980) 159-164.
  • J. Boos, Classical and modern methods in summability, Oxford Univ. Press, Oxford, 2000.
  • J. Borsik, T. Salat, On F-continuity of real functions, Tarta Mt. Math. Publ., 2(1993) 37-42.
  • R. Brown and O. Mucuk, Covering groups of non-connected topological groups revisited, Mathematical Proceedings of the Cambridge Philosophical Society, 115 (1994) 97-110.
  • R.C.Buck, Solution of problem 4216, Amer. Math. Monthly, 55, 36 (1948).
  • H. Çakallı, O. Mucuk, On connectedness via a sequential method, Rev. Un. Mat. Argentina, Revista de la Unio'n Matema’tica Argentina, 54-2 (2013) 101-109.
  • H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett., 25 (2012) 461-465.
  • H. Çakallı, On G-continuity, Comput. Math. Appl., 61 (2011) 313-318.
  • H. Çakallı, New kinds of continuities, Comput. Math. Appl, 61 (2011) 960-965.
  • H. Çakallı, Sequential definitions of compactness, Appl. Math. Lett., 21 , 6 (2008) 594-598.
  • H. Çakallı, B. Thorpe, On summability in topological groups and a theorem of D.L.Prullage, Ann Soc. Math. Pol. Comm. Math., Ser. I, 29 (1990) 139-148.
  • J. Connor, K.-G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. , 33, 1 (2003) 93-121.
  • M. Dik, I. Canak, New Types of Continuities, Abstr. Appl. Anal. Hindawi Publ. Corp., New York, ISSN V. (2010) 1085-3375.
  • F. Gençoğlu, Sequential continuity, compactness and connectedness, Erciyes University , MSc Thesis, June 2013 (in Turkish).​
  • T.B. Iwinski, Some remarks on Toeplitz methods and continuity, Comment.Math. Prace Mat., 17 (1972) 37-43.
  • S. Lin, L. Liu, G-methods, G-spaces and G-continuity in topological spaces, Topology Appl., 212 (2016) 29-48.
  • G. Di Maio, L.D.R. Kocinac, Statistical convergence in topology, Topology Appl., 156 (2008) 28-45.
  • O. Mucuk, Topoloji and Kategory, Nobel Yayınları, Ankara 2011 (in Turkish).
  • O. Mucuk, H. Cakalli, G-connectedness for topological groups with operations, Filomat, 32:3 (2018) 1079-1089.
  • O. Mucuk and H. Çakallı, On G-compactness of topological groups with operations, Filomat, 36:20 (2022) 7113-7121.
  • O. Mucuk, T. Şahan, On G-sequential Continuity, Filomat, 28-6 (2014) 1181-1189.
  • E.C. Posner, Summability preserving functions, Proc.Amer.Math.Soc., 12 (1961) 73-76.
  • V.K.Srinivasan, An equivalent condition for the continuity of a function, Texas J. Sci., 32 (1980) 176-177.
  • E. Spigel, N. Krupnik, On the A-continuity of real functions, J. Anal., 2 (1994) 145-155.
  • E. Öztürk, On almost-continuity and almost A-continuity of real functions, Commun. Fac. Sci. Univ. Ank. See’r. A1 Math. Stat. 32 (1983) 25-30.
  • E. Savaş, G.Das, On the A-continuity of real functions, İstanbul Univ. Fen Fak. Mat Derg. 53 (1994) 61-66.
  • E. Savaş, On invariant continuity and invariant A-continuity of real functions J.Orissa Math.Soc., 3 (1984) 83-88.
  • M. B. Teke, Sequentially continuity, compactness and connectedness in product spaces, Erciyes University, MSc Thesis, August 2023 (in Turksih).

About sequentially open and closed subsets in product spaces

Year 2023, Volume: 5 Issue: 2, 41 - 46, 30.11.2023

Osman Mucuk Mina Betül Teke

https://doi.org/10.47087/mjm.1301293

Abstract

We remind two facts for topological spaces. The one is that in a Hausdorff space $X$ each sequence has a unique limit. This allows us to have a function from the set of all sequences in $X$ to $X$. Another is that in the first countable spaces some topological objects such as open subsets, closed subsets, closures and interiors of the sets, continuous functions and many others can be defined in terms of convergent sequences.

In this paper we compare these notions with their sequential versions in topological spaces. We will take the product spaces into account and give some results.

Keywords

Sequentially convegence product spaces sequentially closed subset sequentiallty hull sequentially closure

References

  • A. Açıkgöz, H. Çakallı, F. Esenbel and LDR Kocinac, A quest of G-continuity in neutrosophic spaces, Mathematical Methods in the Applied Sciences, 44 (9) (2021) 7834-7844.
  • J. Antoni, On the A-continuity of real functions II, Math. Slovaca, 36, No.3 (1986) 283-287.
  • J. Antoni, T. Salat, On the A-continuity of real functions, Acta Math. Univ. Comenian, 39 (1980) 159-164.
  • J. Boos, Classical and modern methods in summability, Oxford Univ. Press, Oxford, 2000.
  • J. Borsik, T. Salat, On F-continuity of real functions, Tarta Mt. Math. Publ., 2(1993) 37-42.
  • R. Brown and O. Mucuk, Covering groups of non-connected topological groups revisited, Mathematical Proceedings of the Cambridge Philosophical Society, 115 (1994) 97-110.
  • R.C.Buck, Solution of problem 4216, Amer. Math. Monthly, 55, 36 (1948).
  • H. Çakallı, O. Mucuk, On connectedness via a sequential method, Rev. Un. Mat. Argentina, Revista de la Unio'n Matema’tica Argentina, 54-2 (2013) 101-109.
  • H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett., 25 (2012) 461-465.
  • H. Çakallı, On G-continuity, Comput. Math. Appl., 61 (2011) 313-318.
  • H. Çakallı, New kinds of continuities, Comput. Math. Appl, 61 (2011) 960-965.
  • H. Çakallı, Sequential definitions of compactness, Appl. Math. Lett., 21 , 6 (2008) 594-598.
  • H. Çakallı, B. Thorpe, On summability in topological groups and a theorem of D.L.Prullage, Ann Soc. Math. Pol. Comm. Math., Ser. I, 29 (1990) 139-148.
  • J. Connor, K.-G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. , 33, 1 (2003) 93-121.
  • M. Dik, I. Canak, New Types of Continuities, Abstr. Appl. Anal. Hindawi Publ. Corp., New York, ISSN V. (2010) 1085-3375.
  • F. Gençoğlu, Sequential continuity, compactness and connectedness, Erciyes University , MSc Thesis, June 2013 (in Turkish).​
  • T.B. Iwinski, Some remarks on Toeplitz methods and continuity, Comment.Math. Prace Mat., 17 (1972) 37-43.
  • S. Lin, L. Liu, G-methods, G-spaces and G-continuity in topological spaces, Topology Appl., 212 (2016) 29-48.
  • G. Di Maio, L.D.R. Kocinac, Statistical convergence in topology, Topology Appl., 156 (2008) 28-45.
  • O. Mucuk, Topoloji and Kategory, Nobel Yayınları, Ankara 2011 (in Turkish).
  • O. Mucuk, H. Cakalli, G-connectedness for topological groups with operations, Filomat, 32:3 (2018) 1079-1089.
  • O. Mucuk and H. Çakallı, On G-compactness of topological groups with operations, Filomat, 36:20 (2022) 7113-7121.
  • O. Mucuk, T. Şahan, On G-sequential Continuity, Filomat, 28-6 (2014) 1181-1189.
  • E.C. Posner, Summability preserving functions, Proc.Amer.Math.Soc., 12 (1961) 73-76.
  • V.K.Srinivasan, An equivalent condition for the continuity of a function, Texas J. Sci., 32 (1980) 176-177.
  • E. Spigel, N. Krupnik, On the A-continuity of real functions, J. Anal., 2 (1994) 145-155.
  • E. Öztürk, On almost-continuity and almost A-continuity of real functions, Commun. Fac. Sci. Univ. Ank. See’r. A1 Math. Stat. 32 (1983) 25-30.
  • E. Savaş, G.Das, On the A-continuity of real functions, İstanbul Univ. Fen Fak. Mat Derg. 53 (1994) 61-66.
  • E. Savaş, On invariant continuity and invariant A-continuity of real functions J.Orissa Math.Soc., 3 (1984) 83-88.
  • M. B. Teke, Sequentially continuity, compactness and connectedness in product spaces, Erciyes University, MSc Thesis, August 2023 (in Turksih).
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Osman Mucuk 0000-0001-7411-2871

Mina Betül Teke 0009-0000-1168-7686

Early Pub Date November 16, 2023
Publication Date November 30, 2023
Acceptance Date November 6, 2023
Published in Issue Year 2023 Volume: 5 Issue: 2

Cite

APA Mucuk, O., & Teke, M. B. (2023). About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics, 5(2), 41-46. https://doi.org/10.47087/mjm.1301293
AMA Mucuk O, Teke MB. About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics. November 2023;5(2):41-46. doi:10.47087/mjm.1301293
Chicago Mucuk, Osman, and Mina Betül Teke. “About Sequentially Open and Closed Subsets in Product Spaces”. Maltepe Journal of Mathematics 5, no. 2 (November 2023): 41-46. https://doi.org/10.47087/mjm.1301293.
EndNote Mucuk O, Teke MB (November 1, 2023) About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics 5 2 41–46.
IEEE O. Mucuk and M. B. Teke, “About sequentially open and closed subsets in product spaces”, Maltepe Journal of Mathematics, vol. 5, no. 2, pp. 41–46, 2023, doi: 10.47087/mjm.1301293.
ISNAD Mucuk, Osman - Teke, Mina Betül. “About Sequentially Open and Closed Subsets in Product Spaces”. Maltepe Journal of Mathematics 5/2 (November 2023), 41-46. https://doi.org/10.47087/mjm.1301293.
JAMA Mucuk O, Teke MB. About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics. 2023;5:41–46.
MLA Mucuk, Osman and Mina Betül Teke. “About Sequentially Open and Closed Subsets in Product Spaces”. Maltepe Journal of Mathematics, vol. 5, no. 2, 2023, pp. 41-46, doi:10.47087/mjm.1301293.
Vancouver Mucuk O, Teke MB. About sequentially open and closed subsets in product spaces. Maltepe Journal of Mathematics. 2023;5(2):41-6.
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