Dini's theorem, the Glossary

Table of Contents

1. 16 relations: Compact space, Continuous function, Cover (topology), Image (mathematics), Jürgen Jost, Mathematical analysis, Mathematics, Monotonic function, Pointwise convergence, Real-valued function, Robert G. Bartle, Sequence, Topological space, Ulisse Dini, Uniform convergence, Walter Rudin.

2. Theorems in real analysis

Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

See Dini's theorem and Compact space

Continuous function

In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.

See Dini's theorem and Continuous function

Cover (topology)

In mathematics, and more particularly in set theory, a cover (or covering) of a set X is a family of subsets of X whose union is all of X. More formally, if C.

See Dini's theorem and Cover (topology)

Image (mathematics)

In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f".

See Dini's theorem and Image (mathematics)

Jürgen Jost

Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry.

See Dini's theorem and Jürgen Jost

Mathematical analysis

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.

See Dini's theorem and Mathematical analysis

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Dini's theorem and Mathematics

Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

See Dini's theorem and Monotonic function

Pointwise convergence

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.

See Dini's theorem and Pointwise convergence

Real-valued function

In mathematics, a real-valued function is a function whose values are real numbers.

See Dini's theorem and Real-valued function

Robert G. Bartle

Robert Gardner Bartle (November 20, 1927 – September 18, 2003) was an American mathematician specializing in real analysis.

See Dini's theorem and Robert G. Bartle

Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

See Dini's theorem and Sequence

Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

See Dini's theorem and Topological space

Ulisse Dini

Ulisse Dini (14 November 1845 – 28 October 1918) was an Italian mathematician and politician, born in Pisa.

See Dini's theorem and Ulisse Dini

Uniform convergence

In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence.

See Dini's theorem and Uniform convergence

Walter Rudin

Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.

See Dini's theorem and Walter Rudin

See also

Theorems in real analysis

• Abel's theorem
• Anderson's theorem
• Arzelà–Ascoli theorem
• Bernstein's theorem on monotone functions
• Blumberg theorem
• Bohr–Favard inequality
• Caristi fixed-point theorem
• Darboux's theorem (analysis)
• Dini's theorem
• Discontinuities of monotone functions
• Dominated convergence theorem
• Extreme value theorem
• Fatou–Lebesgue theorem
• Fermat's theorem (stationary points)
• Fubini's theorem on differentiation
• Fundamental theorem of calculus
• Glaeser's composition theorem
• Hardy's inequality
• Heine–Borel theorem
• Identity theorem
• Implicit function theorem
• Intermediate value theorem
• Inverse function theorem
• Kirszbraun theorem
• Kolmogorov–Arnold representation theorem
• L'Hôpital's rule
• Lagrange inversion theorem
• Lebesgue differentiation theorem
• Lusin's theorem
• Mean value theorem
• Monotone convergence theorem
• Nested intervals
• Riemann series theorem
• Riesz–Fischer theorem
• Rolle's theorem
• Routh–Hurwitz theorem
• Steinhaus theorem
• Sturm's theorem
• Taylor's theorem
• Titchmarsh convolution theorem
• Uniform limit theorem
• Vitali–Carathéodory theorem
• Watson's lemma
• Zahorski theorem
• Śleszyński–Pringsheim theorem

References

[1] https://en.wikipedia.org/wiki/Dini's_theorem

Also known as Dini theorem.