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Yıl 2024, Cilt: 53 Sayı: 1, 88 - 106, 29.02.2024

Yuan Gao Bin Pang

https://doi.org/10.15672/hujms.1205089

Öz

Kaynakça

  • [1] R. Bělohlávek, Fuzzy Relation Systems, Foundation and Principles, Kluwer Academic, Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2002.
  • [2] F. Borceux, Handbook of Categorical Algebra, Vol.2, Cambridge University Press. 1994.
  • [3] J.M. Fang, Stratified $L$-ordered convergence structures, Fuzzy Sets Syst. 161, 2130– 2149, 2010.
  • [4] J.M. Fang, Relationships between $L$-ordered convergence structures and strong $L$-topologies, Fuzzy Sets Syst. 161, 2923–2944, 2010.
  • [5] J.M. Fang and Y. Yue, $\top$-diagonal conditions and continuous extension theorem, Fuzzy Sets Syst. 321, 73–89, 2017.
  • [6] G.S.H. Cruttwell, Normed spaces and the change of base for enriched categories, Ph.D. thesis, Dalhousie University, 2008.
  • [7] U. Höhle, Many Valued Topology and its Applications, Kluwer Academic Publishers, Boston, 2001.
  • [8] U. Höhle, MV-algebra valued filter theory, Quaest. Math. 19, 23–46, 1996.
  • [9] U. Höhle and A.P. Šostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series, vol.3, Kluwer Academic Publishers, Dordrecht, Boston, London, 123–173, 1999.
  • [10] G. Jäger, A category of $L$-fuzzy convergence spaces, Quaest. Math. 24, 501–517, 2001.
  • [11] G. Jäger, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst. 156, 1–24, 2005.
  • [12] G. Jäger, Compactification of lattice-valued convergence spaces, Fuzzy Sets Syst. 161, 10021010, 2010.
  • [13] G. Jäger, Largest and smallest T$_2$-compactifications of lattice-valued convergence spaces, Fuzzy Sets Syst. 190, 32–46, 2012.
  • [14] G. Jäger, Stratified $LMN$-convergence tower spaces, Fuzzy Sets Syst. 282, 62–73, 2016.
  • [15] G. Jäger, Connectedness and local connectedness for lattice-valued convergence spaces, Fuzzy Sets Syst. 300, 134–146, 2016.
  • [16] T. Leinster, Basic Category Theory, Cambridge University Press, 2014.
  • [17] L. Li and Q. Jin, On stratified $L$-convergence spaces: pretopological axioms and diagonal axioms, Fuzzy Sets Syst. 204, 40–52, 2012.
  • [18] L. Li and Q. Jin, $p$-Topologicalness and $p$-regularity for lattice-valued convergence spaces, Fuzzy Sets Syst. 238, 26–45, 2014.
  • [19] L. Li, Q. Jin and K. Hu, On stratified $L$-convergence spaces: Fischer’s diagonal axiom, Fuzzy Sets Syst. 267, 31–40, 2015.
  • [20] B. Pang, On $(L,M)$-fuzzy convergence spaces, Fuzzy Sets Syst. 238, 46–70, 2014.
  • [21] B. Pang, Stratified $L$-ordered filter spaces, Quaest. Math. 40 (5), 661–678, 2017.
  • [22] B. Pang, Categorical properties of $L$-fuzzifying convergence spaces, Filomat, 32 (11), 4021–4036, 2018.
  • [23] B. Pang, Convenient properties of stratified $L$-convergence tower spaces, Filomat, 33 (15), 4811–4825, 2019.
  • [24] B. Pang and Y. Zhao, Several types of enriched $(L,M)$-fuzzy convergence spaces, Fuzzy Sets Syst. 321, 55–72, 2017.
  • [25] G. Preuss, Foundations of Topology, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
  • [26] G. Preuss, Semiuniform convergence spaces, Math. Japon, 41, 465-491, 1995.
  • [27] G. Preuss, The Theory of Topological Structures, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1998.
  • [28] D. Verity, Enriched categories, internal categories and change of base, Repr. Theory Appl. Categ. 20, 1266, 2011.
  • [29] W. Yao, On $L$-fuzzifying convergence spaces, Iran. J. Fuzzy Syst. 6 (1), 63–80, 2009.
  • [30] Q. Yu and J.M. Fang, The category of $\top$-convergence spaces and its Cartesian closedness, Iran. J. Fuzzy Syst. 14, 121–138, 2017.
  • [31] Y.L. Yue and J.M. Fang, The $\top$-filter monad and its applications, Fuzzy Sets Syst. 382, 79–97, 2020.
  • [32] L. Zhang and B. Pang, Monoidal closedness of the category of $\top$-semiuniform convergence spaces, Hacet. J. Math. Stat. 51 (5), 1348–1370, 2022.
  • [33] L. Zhang and B. Pang, A new approach to lattice-valued convergence groups via $\top$- filters, Fuzzy Sets Syst. 455, 198–221, 2023.
  • [34] L. Zhang and B. Pang, Convergence structures in $(L,M)$-fuzzy convex spaces, Filomat, 37 (9), 2859–2877, 2023.

Subcategories of the category of $\top$-convergence spaces

Yıl 2024, Cilt: 53 Sayı: 1, 88 - 106, 29.02.2024

Yuan Gao Bin Pang

https://doi.org/10.15672/hujms.1205089

Öz

$\top$-convergence structures serve as an important tool to describe fuzzy topology. This paper aims to give further investigations on $\top$-convergence structures. Firstly, several types of $\top$-convergence structures are introduced, including Kent $\top$-convergence structures, $\top$-limit structures and principal $\top$-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the ``change of base" approach is applied to $\top$-convergence structures and the relationships between $\top$-convergence structures with respect to different underlying lattices are demonstrated.

Anahtar Kelimeler

T-convergence structure T-filter Kent convergence limit structure change of base

Kaynakça

  • [1] R. Bělohlávek, Fuzzy Relation Systems, Foundation and Principles, Kluwer Academic, Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2002.
  • [2] F. Borceux, Handbook of Categorical Algebra, Vol.2, Cambridge University Press. 1994.
  • [3] J.M. Fang, Stratified $L$-ordered convergence structures, Fuzzy Sets Syst. 161, 2130– 2149, 2010.
  • [4] J.M. Fang, Relationships between $L$-ordered convergence structures and strong $L$-topologies, Fuzzy Sets Syst. 161, 2923–2944, 2010.
  • [5] J.M. Fang and Y. Yue, $\top$-diagonal conditions and continuous extension theorem, Fuzzy Sets Syst. 321, 73–89, 2017.
  • [6] G.S.H. Cruttwell, Normed spaces and the change of base for enriched categories, Ph.D. thesis, Dalhousie University, 2008.
  • [7] U. Höhle, Many Valued Topology and its Applications, Kluwer Academic Publishers, Boston, 2001.
  • [8] U. Höhle, MV-algebra valued filter theory, Quaest. Math. 19, 23–46, 1996.
  • [9] U. Höhle and A.P. Šostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. Höhle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series, vol.3, Kluwer Academic Publishers, Dordrecht, Boston, London, 123–173, 1999.
  • [10] G. Jäger, A category of $L$-fuzzy convergence spaces, Quaest. Math. 24, 501–517, 2001.
  • [11] G. Jäger, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst. 156, 1–24, 2005.
  • [12] G. Jäger, Compactification of lattice-valued convergence spaces, Fuzzy Sets Syst. 161, 10021010, 2010.
  • [13] G. Jäger, Largest and smallest T$_2$-compactifications of lattice-valued convergence spaces, Fuzzy Sets Syst. 190, 32–46, 2012.
  • [14] G. Jäger, Stratified $LMN$-convergence tower spaces, Fuzzy Sets Syst. 282, 62–73, 2016.
  • [15] G. Jäger, Connectedness and local connectedness for lattice-valued convergence spaces, Fuzzy Sets Syst. 300, 134–146, 2016.
  • [16] T. Leinster, Basic Category Theory, Cambridge University Press, 2014.
  • [17] L. Li and Q. Jin, On stratified $L$-convergence spaces: pretopological axioms and diagonal axioms, Fuzzy Sets Syst. 204, 40–52, 2012.
  • [18] L. Li and Q. Jin, $p$-Topologicalness and $p$-regularity for lattice-valued convergence spaces, Fuzzy Sets Syst. 238, 26–45, 2014.
  • [19] L. Li, Q. Jin and K. Hu, On stratified $L$-convergence spaces: Fischer’s diagonal axiom, Fuzzy Sets Syst. 267, 31–40, 2015.
  • [20] B. Pang, On $(L,M)$-fuzzy convergence spaces, Fuzzy Sets Syst. 238, 46–70, 2014.
  • [21] B. Pang, Stratified $L$-ordered filter spaces, Quaest. Math. 40 (5), 661–678, 2017.
  • [22] B. Pang, Categorical properties of $L$-fuzzifying convergence spaces, Filomat, 32 (11), 4021–4036, 2018.
  • [23] B. Pang, Convenient properties of stratified $L$-convergence tower spaces, Filomat, 33 (15), 4811–4825, 2019.
  • [24] B. Pang and Y. Zhao, Several types of enriched $(L,M)$-fuzzy convergence spaces, Fuzzy Sets Syst. 321, 55–72, 2017.
  • [25] G. Preuss, Foundations of Topology, Kluwer Academic Publishers, Dordrecht, Boston, London, 2002.
  • [26] G. Preuss, Semiuniform convergence spaces, Math. Japon, 41, 465-491, 1995.
  • [27] G. Preuss, The Theory of Topological Structures, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1998.
  • [28] D. Verity, Enriched categories, internal categories and change of base, Repr. Theory Appl. Categ. 20, 1266, 2011.
  • [29] W. Yao, On $L$-fuzzifying convergence spaces, Iran. J. Fuzzy Syst. 6 (1), 63–80, 2009.
  • [30] Q. Yu and J.M. Fang, The category of $\top$-convergence spaces and its Cartesian closedness, Iran. J. Fuzzy Syst. 14, 121–138, 2017.
  • [31] Y.L. Yue and J.M. Fang, The $\top$-filter monad and its applications, Fuzzy Sets Syst. 382, 79–97, 2020.
  • [32] L. Zhang and B. Pang, Monoidal closedness of the category of $\top$-semiuniform convergence spaces, Hacet. J. Math. Stat. 51 (5), 1348–1370, 2022.
  • [33] L. Zhang and B. Pang, A new approach to lattice-valued convergence groups via $\top$- filters, Fuzzy Sets Syst. 455, 198–221, 2023.
  • [34] L. Zhang and B. Pang, Convergence structures in $(L,M)$-fuzzy convex spaces, Filomat, 37 (9), 2859–2877, 2023.
Toplam 34 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Yuan Gao Bu kişi benim 0000-0003-1083-0879

Bin Pang 0000-0001-5092-8278

Erken Görünüm Tarihi 10 Ocak 2024
Yayımlanma Tarihi 29 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 1

Kaynak Göster

APA Gao, Y., & Pang, B. (2024). Subcategories of the category of $\top$-convergence spaces. Hacettepe Journal of Mathematics and Statistics, 53(1), 88-106. https://doi.org/10.15672/hujms.1205089
AMA Gao Y, Pang B. Subcategories of the category of $\top$-convergence spaces. Hacettepe Journal of Mathematics and Statistics. Şubat 2024;53(1):88-106. doi:10.15672/hujms.1205089
Chicago Gao, Yuan, ve Bin Pang. “Subcategories of the Category of $\top$-Convergence Spaces”. Hacettepe Journal of Mathematics and Statistics 53, sy. 1 (Şubat 2024): 88-106. https://doi.org/10.15672/hujms.1205089.
EndNote Gao Y, Pang B (01 Şubat 2024) Subcategories of the category of $\top$-convergence spaces. Hacettepe Journal of Mathematics and Statistics 53 1 88–106.
IEEE Y. Gao ve B. Pang, “Subcategories of the category of $\top$-convergence spaces”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, ss. 88–106, 2024, doi: 10.15672/hujms.1205089.
ISNAD Gao, Yuan - Pang, Bin. “Subcategories of the Category of $\top$-Convergence Spaces”. Hacettepe Journal of Mathematics and Statistics 53/1 (Şubat 2024), 88-106. https://doi.org/10.15672/hujms.1205089.
JAMA Gao Y, Pang B. Subcategories of the category of $\top$-convergence spaces. Hacettepe Journal of Mathematics and Statistics. 2024;53:88–106.
MLA Gao, Yuan ve Bin Pang. “Subcategories of the Category of $\top$-Convergence Spaces”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 1, 2024, ss. 88-106, doi:10.15672/hujms.1205089.
Vancouver Gao Y, Pang B. Subcategories of the category of $\top$-convergence spaces. Hacettepe Journal of Mathematics and Statistics. 2024;53(1):88-106.

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