The converse of the intermediate value theorem: from Conway to Cantor to cosets and beyond

zbMath1311.26002MaRDI QIDQ2261887

Greg G. Oman

Publication date: 13 March 2015

Published in: Missouri Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.mjms/1418931955

zbMATH Keywords

Cantor setultrafilterintermediate value theoremcosetConway base 13 function

Mathematics Subject Classification ID

Special maps on topological spaces (open, closed, perfect, etc.) (54C10) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25)

Related Items (7)

Graphs of real functions with pathological behaviors ⋮ Continuity between Cauchy and Bolzano: issues of antecedents and priority ⋮ Unnamed Item ⋮ The reverse of the intermediate value theorem in some topological spaces ⋮ Insights and Observations on Teaching the Intermediate Value Theorem ⋮ The intermediate value theorem and decision-making in psychology and economics: an expositional consolidation ⋮ On the girth of three-dimensional algebraically defined graphs with multiplicatively separable functions

Cites Work

• Resolvability: A selective survey and some new results
• Tychonoff expansions with prescribed resolvability properties
• Toward a More Complete List of Completeness Axioms
• On maximally resolvable spaces
• Some Sufficient Conditions for Maximal-Resolvability⁽¹⁾
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