Mild Continuity Properties of Relations and Relators in Relator Spaces

Száz, Árpád; Zakaria, Amr

doi:10.1007/978-3-319-31338-2_16

Cited by 5 publications

(9 citation statements)

References 20 publications

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“…Finally, we note that, by [209,Theorem 32] and [135, Theorem 1.5] , the following two theorems are also true.…”

Section: Further Theorems On Regular Structuresmentioning

confidence: 82%

“…( For their theories and applications, see [14,64,59,33,36] . ) Some examples and generalizations of Galois and Pataki connections can also be found in [179,183,20,194,198,202] and [190,206,209,199,203] . However, it is frequently enough to consider such connections only for corelations.…”

Section: A Few Basic Facts On Ordered Setsmentioning

confidence: 99%

“…The importance of the dense sets is well-established in topology. However, the fat sets have formerly been explicitly used only by the second author in [166,169,178,182,201] .…”

Section: The Induced Fat and Dense Setsmentioning

confidence: 99%

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Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces

Salih¹,

Száz²

2020

era

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Motivated by some ordinary and extreme connectedness properties of topologies, we introduce several reasonable connectedness properties of relators (families of relations). Moreover, we establish some intimate connections among these properties. More concretely, we investigate relationships among various minimalness (well-chainedness), connectedness, hyper-and ultra-connectedness, door, superset, submaximality and resolvability properties of relators. Since most generalized topologies and all proper stacks (ascending systems) can be derived from preorder relators, the results obtained greatly extends some standard results on topologies. Moreover, they are also closely related to some former results on well-chained and connected uniformities.

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“…Finally, we note that, by [209,Theorem 32] and [135, Theorem 1.5] , the following two theorems are also true.…”

Section: Further Theorems On Regular Structuresmentioning

confidence: 82%

Section: A Few Basic Facts On Ordered Setsmentioning

confidence: 99%

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Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces

Salih¹,

Száz²

2020

era

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“…The above theorem and its corollary show that, analogously to continuity properties of pairs of relations studied in [71], additivity and homogeneity properties of pairs of relations should have also been investigated in Sects. 4-6. Analogously to [53 …”

Section: Remark 63mentioning

confidence: 89%

“…In the theory of generalized uniform spaces, it is quite usual to associate the Davis-Pervin relation F U = U 2 ∪ U c × X with the set U ⊂ X, and more generally the Császár-Hunsaker-Lindgren relation [52,58]. )…”

Section: Theorem 23 If F Is a Subadditive (Left Or Right-quasisubaddimentioning

confidence: 99%

Constructions and Extensions of Free and Controlled Additive Relations

Glavosits

Száz

2014

Handbook of Functional Equations

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By using several auxiliary results on relations and their intersection convolutions, we give some necessary and sufficient conditions in order that a certain additive partial selection relation Φ of a relation F of one group X to another Y could be extended to a total, additive selection relation Ψ of the relation F + Φ(0).The results obtained extend some Hahn-Banach type extension theorems of B. Rodríguez-Salinas, L. Bou, Z. Gajda, A. Smajdor, W. Smajdor, and the second author. Moreover, they can be used to prove some alternate forms of the Hyers-Ulam type selection theorems of Z. Gajda, R. Ger, R. Badora, Zs. Páles, and the second author.Keywords Additive and homogeneous relations · Intersection convolutions of relations · Extensions of additive partial selection relations

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