Continuous action of stratified lattice-valued convergence groups (2nd International Conference on Mathematical Analysis

Abstract

Using the ideas of stratified lattice-valued convergence structure attributed to G. Jager [A category of $L$-fuzzy convergence spaces, Quaest. Math. 24(2001), 501-517], and stratified frame-valued generalized convergence group introduced in [T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame-valued stratified generalized convergence groups, Quaest. Math. 31(2008), 279-302], we present here a notion of continuous action of stratified lattice-valued convergence group on stratified lattice-valued convergnce space. We discuss how stratified lattice-valued convergence group act continuously on a set of contnuous functions bestowed with stratified lattice-valued convergence structure of contnuous convergence of Jager. Finally, we show that there exists a one-to-one correspondence between the homeoporphic representation of stratified lattice-valued convergence group and its continuous actions on a stratified lattice-valued limit space [G. Jager, Subcategories of lattice-valued convergence spaces, International J. Fuzzy Sets and Systems 156(2005),