Results 251 to 260 of about 912,065 (289)

Complete Regularity as a Separation Axiom

Canadian Journal of Mathematics, 1969
Although the axiom of complete regularity ought to be a separation axiom, in none of its usual forms does it look like an intrinsic separation axiom. Our aim in this paper is to establish such characterizations of complete regularity which naturally fit in between regularity and normality and which already have proved to be fundamental and useful. This
de Groot, J., Aarts, J. M.
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Fuzzy delta separation axioms

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), 2011
We introduce a new type of separation axioms, which is called fuzzy δ-separation axioms by using the concept of fuzzy δ-open sets. Also we investigate the relation between the separation property and the subspaces. We show that fuzzy δ-separation axioms are hereditary in fuzzy regular open subspaces.
Seok Jong Lee, Sang Min Yun
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Separation Axioms and Direct Limits

Canadian Mathematical Bulletin, 1969
A topological space X is called a direct limit of a family (Xα) of subspaces of X if and only if(1)(2)If X is a direct limit of an increasing sequence (Xn) of closed subspaces then it is well known and easy to prove that X is a T1-space resp. a T4-space provided all Xn are T1-spaces resp. T4-spaces.
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The Priestley Separation Axiom for Scattered Spaces

Order, 2002
The authors give a new characterization of scattered compact Hausdorff spaces. Main results: (1) Let \(X\) be a scattered compact Hausdorff space with a quasi-order \(R\). Then \(R\) is closed if and only if \((X,R)\) is a Priestley space. (2) Let \(X\) be a non-scattered compact Hausdorff space. Then there is a closed equivalence relation \(E\) on \(X\
Guram Bezhanishvili, Ray Mines, Patrick J. Morandi   +2 more
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Separation Axioms

2022
Avishek Adhikari, Mahima Ranjan Adhikari
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Separation principles and the axiom of determinateness

Journal of Symbolic Logic, 1978
Let Γ be a class of subsets of Baire space (ωω) closed under inverse images by continuous functions. We say such a Γ is continuously closed. Let , the class dual to Γ, consist of the complements relative to ωω of members of Γ. If Γ is not selfdual, i.e., , then let .
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\(sg\)-separation axioms

2007
Summary: \textit{N. Levine} [Rend. Circ. Mat. Palermo, II. Ser. 19, 89--96 (1970; Zbl 0231.54001)] introduced the notion of generalized closed (abbreviated as \(g\)-closed). The complement of a \(g\)-closed set is called \(g\)-open. The purpose of the present work is to define and study new separation axioms using \(g\)-open sets.
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On \(m\)-\(D\)-separation axioms

2012
Summary: We introduce the notions of \(m\)-\(D\)-sets and some lower separation axioms \(m\)-\(D_i\) (\(i=0,1,2\)) on \(m\)-structures, which are weaker than topological structures, and obtain a unified theory of separation axioms \(D_i\), \(s\)-\(D_i\), \(p\)-\(D_i\), \(\theta\)-\(D_i\), \(\delta\)-semi\(D_i\), \(\delta\)-pre\(D_i\) (\(i=0,1,2\)) in ...
NOIRI, Takashi, POPA, Valeriu
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Notes on separation axioms in hyperspaces

2000
Usually, hyperspace topologies are studied in \(T_1\)-spaces but in this paper no separation axioms are assumed. Moreover, the authors start with general proximities in the base space in sharp contrast to most of the literature where only metric proximities are considered.
DI CAPRIO D, MECCARIELLO E
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Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms

Mathematics, 2022
A A Azzam, JOSÉ Carlos R Alcantud, T M Al-Shami   +2 more
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