Separation, connectedness, and disconnectedness

DOI10.55730/1300-0098.3360OpenAlexW4317607734MaRDI QIDQ5882012

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Publication date: 14 March 2023

Published in: Turkish Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.55730/1300-0098.3360

zbMATH Keywords

closure operatorconnected spacestotally disconnected spaces\(T_2\) spaceshereditarily disconnected spaces

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) Special categories (18B99) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15)

Related Items (1)

Closure operators, irreducibility, Urysohn's lemma, and Tietze extension theorem for proximity spaces

Cites Work

• Separation versus connectedness
• Quotient-reflective and bireflective subcategories of the category of preordered sets
• \(\text{Pre}T _{2}\) objects in topological categories
• Closure operators. I
• Convenient categories for internal singular algebraic topology
• Separation properties
• Completely regular objects and normal objects in topological categories
• Closure operators and connectedness
• \(T_ 2\)-objects in topological categories
• Closedness, separation and connectedness in pseudo-quasi-semi metric spaces
• Closure operators in convergence approach spaces
• T4, Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces
• Sober spaces
• Closure operators in semiuniform convergence spaces
• Closure operators in convergence spaces
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