T4, Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces

DOI10.3906/MAT-2012-101zbMath1500.54001OpenAlexW3149588173WikidataQ125017572 ScholiaQ125017572MaRDI QIDQ5100243

Ayhan Ercıyes, Tesnim Meryem Baran

Publication date: 29 August 2022

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-2012-101

zbMATH Keywords

topological categoryTietze extensionUrysohn property\(T_1\) objects\(T_4\) objectsconstant filter convergence spaceslocal \(T_4\)

Mathematics Subject Classification ID

Topological spaces and generalizations (closure spaces, etc.) (54A05) Categorical methods in general topology (54B30) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Extension of maps (54C20) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15)

Related Items (3)

Separation, connectedness, and disconnectedness ⋮ Closure operators, irreducibility, Urysohn's lemma, and Tietze extension theorem for proximity spaces ⋮ Sober spaces

Cites Work

• Compactness, perfectness, separation, minimality and closedness with respect to closure operators
• Separation properties
• \(T_3\) and \(T_4\)-objects in topological categories
• Completely regular objects and normal objects in topological categories
• Initially Structured Categories and Cartesian Closedness
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