ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES

Document Type: Research Paper

Author

School of Mechanical Engineering, University of Applied Sciences Stralsund, D-18435 Stralsund, Germany

Abstract

In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our category to the categories of stratified $L$-topological spaces and of enriched $LM$-fuzzy topological spaces.

Keywords


[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, 1989.
[2] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets and Systems, 157 (2006), 820 {
831.
[3] P. V. Flores, R. N. Mohapatra and G. Richardson, Lattice-valued spaces: fuzzy convergence,
Fuzzy Sets and Systems, 157 (2006), 2706 { 2714.
[4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A Compendium
of Continuous Lattices, Springer-Verlag Berlin Heidelberg, 1980.
[5] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: U. Hohle,
S.E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory,
Kluwer, Boston/Dordrecht/London 1999, 123 { 272.
[6] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501 { 518.
[7] G. Jager, A note on strati ed LM- lters, Iranian Journal of Fuzzy Systems, 10(4) (2013),
135 { 142.
[8] G. Jager, Strati ed LMN-convergence tower spaces, Fuzzy Sets and Systems, 282 (2016), 62
{ 73.
[9] K. Keimel and J. Lawson, Continuous and Completely Distributive Lattices, in: Lattice
Theory: Special Topics and Applications Vol. 1 (G. Gratzer, F. Wehring (Eds.)), Birkhauser
Basel 2014, 5-53.
[10] B. Pang, Enriched (L,M)-fuzzy convergence spaces, Journal of Intelligent & Fuzzy Systems,
27 (2014), 93 { 103.
[11] B. Pang and Y. Zhao, Strati ed (L,M)-fuzzy Q-convergence spaces, Iranian Journal Fuzzy
Systems, 13(4) (2016), 95 { 111.
[12] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983.
[13] W. Yao, Moore-Smith convergence in (L, M)-fuzzy topology, Fuzzy Sets and Systems, 190
(2012), 47 { 62.