Real functions and near-normal spaces

Shchepin, E. V.

doi:10.1007/bf00968394

Cited by 27 publications

(18 citation statements)

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“…It would be interesting to know if the converse of this is valid or if the converse of Theorem 3.2 is true. Shchepin [14] gave an example of a mildly normal space X such that X x I is not mildly normal.…”

Section: Then V Is a Continuous Function Defined On X If H = F -V Tmentioning

confidence: 99%

PM-normality and the insertion of a continuous function

Lane¹

1979

Pacific J. Math.

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Section: Then V Is a Continuous Function Defined On X If H = F -V Tmentioning

confidence: 99%

PM-normality and the insertion of a continuous function

Lane¹

1979

Pacific J. Math.

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“…Shchepin introduced the same notion in the class of regular spaces, see [6], he called it κ-normality. It is clear from the definitions that any normal space is mildly normal.…”

Section: Definition: (Singal and Singal)mentioning

confidence: 99%

beta;-normal topological spaces

Lutfi¹

2008

Filomat

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A topological space X is called π-normal if for any two disjoint closed subsets A and B of X one of which is π-closed, there exist two open disjoint subsets U and V of X such that A ⊆ U and B ⊆ V. We will present some characterizations of π-normality and some examples to show relations between π-normality and other weaker version of normality such as mild normality, almost normality, and quasi-normality. We investigate in this paper a weaker version of normality called π-normality. We will prove that π-normality is a property which lies between almost normality and normality. We will present some characterizations of π-normality and some examples to show relations between π-normality and other weaker versions of normality such as mild normality, almost normality, and quasi-normality. We will denote an ordered pair by x, y , the set of positive integers by N and the set of real numbers by R. A T 4 space is a T 1 normal space and a Tychonoff space is a T 1 completely regular space. The interior of a set A will be denoted by intA, and the closure of a set A will be denoted by A.

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“…Compare with construction of II [13]. Using the quotient topology, let These spaces were studied systematically in [19] and [21] and called K-normal and mildly normal respectively. THEOREM 4.2 [19] and [21] use, available at https://www.cambridge.org/core/terms.…”

Section: I) a Dense Subset Of An Open Set Is R*-embedded If Given Twomentioning

confidence: 99%

“…Using the quotient topology, let These spaces were studied systematically in [19] and [21] and called K-normal and mildly normal respectively. THEOREM 4.2 [19] and [21] use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446788700031396 (6] Some embeddings related to C*-embeddings 93…”

Section: I) a Dense Subset Of An Open Set Is R*-embedded If Given Twomentioning

confidence: 99%