Proximity Ordered Spaces

Singal, M. K.; Lal, Sunder

doi:10.1112/jlms/s2-14.3.393

Cited by 8 publications

(8 citation statements)

References 5 publications

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“…Let Q be the set of the rational numbers, and, for x, yER, define Since the cited lemma is used essentially in the proof of Theorem 3.1 of [15] (which states that r(6*) is always regularly preordered), this latter is probably also incorrect.…”

Section: On a False Lemma Of Singal And Sunder Lalmentioning

confidence: 96%

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Syntopogenous spaces with preorder. IV (regularity, normality)

Matolcsy¹

1985

Acta Math Hung

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Section: On a False Lemma Of Singal And Sunder Lalmentioning

confidence: 96%

“…A preordered topological space is normally preordered iff its "classical" associated is normally preordered in the sense of Nachbin ([13], p. 28; see also e.g. [7], [12], [15] PROOF. Assume that (E, 90, <=) is normally preordered.…”

Section: Normally Preordered Spacesmentioning

confidence: 99%

Syntopogenous spaces with preorder. IV (regularity, normality)

Matolcsy¹

1985

Acta Math Hung

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“…Recall that: a space X is said to be mildly normal [22], if any pair of disjoint closed domain subsets A and B of X can be separated. The converse of Corollary 4 is not true in general as shown by the next example: is a Tychonoff, L-normal and CC-normal space, which is neither mildly normal nor locally compact [14].…”

Section: Preliminariesmentioning

confidence: 99%

CC-Tychonoffness, CCT3 and CC-Almost Regularity

Thabit¹,

Alqurashi

2023

Eur. J. Pure Appl. Math.

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Following the notion of so-called C-normality - a weaker version of normality in topological spaces as proposed by A. V. Arhangel’skii, further weaker version called CC-normality is studied by Kalantan et al [14]. In this paper, we investigate various type of properties such as CC-complete regularity, CC-almost complete regularity, CC-regularity, CC-almost regularity, CCT3 and CC-Tychonoffness. A space (X, T ) is called a CC-completely regular (resp. CC-almost completely regular, CC-regular, CC-almost regular, CCT3, CC-Tychonoff) space if there exist a completely regular (resp. almost completely regular, regular, almost regular, T3, Tychonoff) space Y and a bijective function f : X → Y such that the restriction function f|A : A → f(A) is a homeomorphism for each countably compact subspace A ⊆ X. We study these properties and present some examples to illustrate the relationships among them with other forms of topological properties.

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“…| (1.3) REMARKS. For the "classical" topological structures we have the following connections (see also [1], [2], [9], [10], [13], [14], and [11], p. 58).…”

Section: 1) ~ (~) Is An Increasing (Decreasing) Biperfect Topogenoumentioning

confidence: 99%

Syntopogenous spaces with preorder. I (Convexity)

Matolcsy

1984

Acta Math Hung

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The present paper is a member of a sequence of notices dealing with syntopogenous spaces equipped with a preorder. Starting out from the analogous properties of topological ([11]), proximity ([14]) and uniform ([11], [12]) ordered spaces, this direction of the research was taken the initiative by Burgess--The examinations of this publication connect with the results of these authors, and study two general types of convexity of preordered syntopogenous spaces.I am very grateful to Professor A. Cs~szfir for this valuable advices.

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Proximity Ordered Spaces

Cited by 8 publications

References 5 publications

Syntopogenous spaces with preorder. IV (regularity, normality)

Syntopogenous spaces with preorder. IV (regularity, normality)

CC-Tychonoffness, CCT3 and CC-Almost Regularity

Syntopogenous spaces with preorder. I (Convexity)

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