An Illustration of the Power of Structure Theory

Hofmann, Karl Heinrich

doi:10.1007/978-94-017-2529-3_8

Cited by 1 publication

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“…Similarly, the continuity of a follows from the observation: In classical theory of topological semigroups, the following result is known as Ellis's Lemma [14](see also [41]). This result has been incorporated for classical convergence semigroup in [17].…”

Section: Complete Heyting Algebra-valued Convergencementioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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Complete Heyting algebra-valued convergence semigroups

Ahsanullah

Al-Thukair

2018

Filomat

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Considering a complete Heyting algebra H, we introduce a notion of stratified H-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified H-convergence semigroup is a stratified H-convergence group. We supply a variety of natural examples; and show that every stratified H-convergence semigroup with identity is a stratified H-quasiuniform convergence space. We also show that given a commutative cancellative semigroup equipped with a stratified H-quasi-unifom structure satisfying a certain property gives rise to a stratified H-convergence semigroup via a stratified H-quasi-uniform convergence structure.

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Section: Complete Heyting Algebra-valued Convergencementioning

confidence: 99%