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Abstract and Applied Analysis
Volume 2014, Article ID 328153, 11 pages
Research Article

Lattice-Valued Convergence Spaces: Weaker Regularity and -Regularity

1Department of Mathematics, Liaocheng University, Liaocheng 252059, China
2College of Mathematics and Econometrics, Hunan University, Changsha 410082, China

Received 5 September 2013; Accepted 7 December 2013; Published 12 January 2014

Academic Editor: Abdelghani Bellouquid

Copyright © 2014 Lingqiang Li and Qiu Jin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By using some lattice-valued Kowalsky’s dual diagonal conditions, some weaker regularities for Jäger’s generalized stratified -convergence spaces and those for Boustique et al’s stratified -convergence spaces are defined and studied. Here, the lattice is a complete Heyting algebra. Some characterizations and properties of weaker regularities are presented. For Jäger’s generalized stratified -convergence spaces, a notion of closures of stratified -filters is introduced and then a new -regularity is defined. At last, the relationships between -regularities and weaker regularities are established.