Enriched lattice-valued convergence groups

Complete Heyting algebra-valued convergence semigroups

“…It is shown in Proposition 3.3 [2](see also, Lemma 2.9 and Proposition 2.10 [3]) that F G = m ⇒ (F × G) is a stratified H-filter on X.…”

“…[32][33][34][35]45]), we generalized the notion of convergence groups into the context of frame-valued convergence groups [2] and later, lattice-valued convergence ring and its uniform convergence structures [1]. Furthermore, we studied enriched lattice-valued convergence groups in [3]. All of these works are based on lattice-valued filter-theoretic convergence structures attributed to G. Jäger undertaken since 2001(cf.…”

“…This has stimulated our interest further to look for lattice-valued convergence semigroups based on whatever we found from existing papers on classical convergence semigroups [17,18]. In this paper, we intend to develop a basic theory on lattice-valued convergence semigroups; unlike previous findings [1][2][3], here classical results on semigroup theory are particularly used like their classical counterpart [9,11,14,40,41,44,49].…”

“…Also, for any F ∈ F s H (X), we define a map Υ l F : H X×X −→ H defined by The proof of this theorem follows from the following construction, for details see Theorem 5.6 [3]. If we define the map…”