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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 2

Separation, compactness, and sobriety in the category of constant limit spaces

Ayhan Erciyes(Aksaray Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü)0000-0002-0942-5182
Muhammad Qasım(Department of Mathematics, School of Natural Sciences, National University of Sciences \& Technology)0000-0001-9485-8072
İsmail Alper Güvey(AKSARAY ÜNİVERSİTESİ)0009-0008-6165-643X
Sayfa
—
Yayın Tarihi
2024-06-21
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we compare our results in some topological categories.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The objective of this article is to characterize each of compact, sober, and $T_{i}$ for $i=0,1,2$ constant limit spaces as well as to investigate the relationships between them.
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Temel Bulgular & Veri:The objective of this article is to characterize each of compact, sober, and $T_{i}$ for $i=0,1,2$ constant limit spaces as well as to investigate the relationships between them.
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Sonuç & Katkı:Finally, we compare our results in some topological categories.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Topological category · closure operator · sober object

Abstract

The objective of this article is to characterize each of compact, sober, and $T_{i}$ for $i=0,1,2$ constant limit spaces as well as to investigate the relationships between them. Finally, we compare our results in some topological categories.

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Bu Makaleye Atıf Yap

Erciyes, A., Qasım, M., Güvey, İ. A. (2024). Separation, compactness, and sobriety in the category of constant limit spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 2. https://doi.org/10.31801/cfsuasmas.1336733

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Kaynakça (26)

  1. Adamek, J., Herrlich. H., Strecker, G. E., Abstract and Concrete Categories, Pure and Applied Mathematics, John Wiley & Sons, New York, 1990.
  2. Baran, M., Separation properties, Indian Journal Pure Applied Mathematics, 23 (1991), 333–341.
  3. Baran, M., Stack and filters, Turkish Journal of Mathematics, 16 (1992), 95–108.
  4. Baran M., The notion of closedness in topological categories. Commentationes Mathematicae Universitatis Carolinae, 34 (2) (1993), 383–395.
  5. Baran, M., Separation properties in categories of constant convergence spaces, Turkish Journal of Mathematics, 18 (1994), 238–248.
  6. Baran, M., Altındiş, H., $T_{2}$–objects in topological categories, Acta Mathematica Hungarica 71 (1996), 41–48.
  7. Baran, M., A notion of compactness in topological categories, Publicationes Mathematicae Debrecen, 50 (1997), 221–234.
  8. Baran M., Completely regular objects and normal objects in topological categories. Acta Mathematica Hungarica, 80 (1998), 211–224.
  9. Baran, M., Closure operators in convergence spaces, Acta Mathematica Hungarica, 87 (2000), 33–45. https://doi.org/10.1023/a:1006768916033
  10. Baran, M., Kula, M., A note on separation and compactness in categories of convergence spaces, Applied General Topology, 4 (1) (2003), 1–13. https://doi.org/10.4995/agt.2003.2005
  11. Baran, M., $PreT_{2}$ objects in topological category, Applied Category Structures, 17 (2009), 591–602. https://doi.org/10.1007/s10485-008-9161-4
  12. Baran, M., Abughalwa, H., Sober spaces, Turkish Journal of Mathematics, 46 (2022), 299–310. https://doi.org/10.3906/mat-2109-95
  13. Baran, M., Separation, connectedness, and disconnectedness, Turkish Journal of Mathematics, 47 (1) (2023), 279–295. https://doi.org/10.55730/1300-0098.3360
  14. Baran, M., Stone spaces I, Filomat, 38 (2024).
  15. Baran, T. M., Local $T_{2}$ extended pseudo-quasi-semi metric spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (2) (2019), 2117–2127. https://doi.org/10.31801/cfsuasmas.497701
  16. Baran, T. M., Closedness, separation and connectedness in pseudo-quasi-semi metric spaces, Filomat, 34 (14) (2020), 4757–4766. https://doi.org/10.2298/FIL2014757B
  17. Binz, E., Keller, H. H., Kunktionenraume in der Kategorie der Limesraume, no. 383 in Sero AI. Ann. Acad. Sci. Fennicae, 1966.
  18. Dieudonne, J. A., Grothendieck A. Elements de Geometrie Algebrique, Springer, New York, 1971.
  19. Dikranjan, D., Tholen, W., Categorical Structure of Closure Operators, Kluwer Academic Publishers, Dordrecht, 1995.
  20. Erciyes, A., Baran, T. M., Qasim, M., Closure operators in constant filter convergence spaces, Konuralp Journal of Mathematics, 8 (1) (2020), 185–191.
  21. Erciyes, A., Baran, T. M., $T_{4}$, Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces, Turkish Journal of Mathematics, 45 (2021), 843–855. https://doi.org/10.3906/mat-2012-101
  22. Frölicher, A., Bucher, W., Calculus in Vector Spaces without Norm, Lecture Notes in Mathematics, 1966.
  23. Kula, M., Baran, T. M., Separation axioms, Urysohn’s lemma and Tietze extention theorem for extended pseudo-quasi-semi metric spaces, Filomat, 36 (2) (2022), 703–713. https://doi.org/10.2298/FIL2202703B
  24. Ozkan, S., Kula, M., Kula, S., Baran, T. M., Closure operators, irreducibility, Urysohn’s lemma, and Tietze extension theorem for proximity spaces, Turkish Journal of Mathematics, 47 (1) (2023), 870–882. https://doi.org/10.55730/1300-0098.3398
  25. Qasim, M., Baran, M., $T_{1}$ approach spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68 (1) (2019), 784–800. https://doi.org/10.31801/cfsuasmas.478632
  26. Qasim, M., Baran, M., Abughalwa, H., Closure operators in convergence approach spaces, Turkish Journal of Mathematics, 45 (2021), 139–152. https://doi.org/10.3906/mat-2008-6