Basic Tools, Increasing Functions, and Closure Operations in Generalized Ordered Sets

Száz, Árpád

doi:10.1007/978-3-319-31317-7_28

Cited by 10 publications

(10 citation statements)

References 25 publications

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“…Therefore, the study of decreasing functions can be traced back to that of the increasing ones. In [40], by proving the following statements, we have shown that almost the same is true in connection with the strictly increasing ones.…”

Section: Increasing Functions Of One Goset To Anothermentioning

confidence: 56%

“…In [40], concerning strictly increasing functions, we have also proved Theorem 4.5. If f is a strictly increasing function of a linear goset X onto an antisymmetric one Y, then…”

Section: Theorem 43 For a Function F Of One Goset X To Another Y The Following Assertions Holdmentioning

confidence: 67%

“…Several interesting characterizations of increasingly regular and normal functions have also been established in [31,35]. Moreover, some closely related results for increasing functions and closure operations have also been proved in [40]. Now, by improving and extending some of these results, we shall, for instance, prove that for a function f of a sup-complete proset X to an arbitrary one Y, the following assertions are equivalent: (1) f is increasingly normal,…”

Section: Introductionmentioning

confidence: 86%

“…) Moreover, it is noteworthy that if X and Y are supposed to be only arbitrary gosets, then (1) already implies the second statement of (6). In [40], for a function f of one goset X to another, we have only prove that f is increasing if and only if…”

Section: Introductionmentioning

confidence: 99%

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Galois and Pataki Connections on Generalized Ordered Sets

Száz

2019

EJMS

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In this paper, having in mind Galois and Pataki connections, we establish several basic theorems on increasingly seminormal and semiregular functions between gosets. An ordered pair X(\leq )=(X,\leq ) consisting of a set X and a relation ≤ on X is called a goset (generalized ordered set). A function f of one goset X to another Y is called increasingly upper g-seminormal, for some function g of Y to X, if f(x)\leq y implies x \leq g(y). While, the function f is called increasingly upper φ-semiregular, for some function φ of X to itself, if f(u)\leq f(v) implies u\leq \varphi (v). The increasingly lower seminormal (semiregular) functions are defined by the reverse implications. Moreover, a function is called increasingly normal (regular) if it is both increasingly upper and lower seminormal (semiregular). The results obtained extend and supplement several former results of O. Ore and the present author on Galois and Pataki connections. Namely, the pairs (f, g) and (f, φ) may be called increasing Galois and Pataki connections if the function f is increasingly g-normal and φ-regular, respectively.

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Section: Increasing Functions Of One Goset To Anothermentioning

confidence: 56%

“…In [40], concerning strictly increasing functions, we have also proved Theorem 4.5. If f is a strictly increasing function of a linear goset X onto an antisymmetric one Y, then…”

Section: Theorem 43 For a Function F Of One Goset X To Another Y The Following Assertions Holdmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

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Galois and Pataki Connections on Generalized Ordered Sets

Száz

2019

EJMS

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“…A relator R on X to Y , or a relator space (X , Y )(R) , is called simple if R = {R} for some relation R . Simple relator spaces X (R) and (X , Y )(R) were called gosets and formal context in [197] and [59] , respectively.…”

Section: A Few Basic Facts On Relatorsmentioning

confidence: 99%

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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Birelator Spaces Are Natural Generalizations of Not Only Bitopological Spaces, But Also Ideal Topological Spaces

Száz

2019

Mathematical Analysis and Applications

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Basic Tools, Increasing Functions, and Closure Operations in Generalized Ordered Sets

Cited by 10 publications

References 25 publications

Galois and Pataki Connections on Generalized Ordered Sets

Galois and Pataki Connections on Generalized Ordered Sets

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

Birelator Spaces Are Natural Generalizations of Not Only Bitopological Spaces, But Also Ideal Topological Spaces

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