the Heine–Cantor theorem states that a continuous function between two metric spaces is uniformly continuous if its domain is compact. The theorem is named...

Andréief–Heine identity Heine–Borel theorem Heine–Cantor theorem Heine definition of continuity Heine's Reciprocal Square Root Identity Heine–Stieltjes...

on a compact interval I is necessarily uniformly continuous (the Heine–Cantor theorem) admits a succinct hyperreal proof. Let x, y be hyperreals in the...

real numbers are more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He...

Andréief–Heine identity Heine–Borel theorem Heine–Cantor theorem Heine–Stieltjes polynomials Heine definition of continuity Heine functions Heine's identity...

non-empty intersection Heine–Cantor theorem: a continuous function on a compact space is uniformly continuous Cantor–Bendixson theorem: a closed set of a...

Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis...

metric to the integers endowed with the usual Euclidean metric. The Heine–Cantor theorem asserts that every continuous function on a compact set is uniformly...

Cantor–Bernstein theorem Cantor–Dedekind axiom Heine–Cantor theorem Cantor–Schröder–Bernstein theorem Cantor–Schröder–Bernstein property Smith–Volterra–Cantor set...

logic) Cantor–Bernstein–Schröder theorem (set theory, cardinal numbers) Cantor's theorem (set theory, Cantor's diagonal argument) Church–Rosser theorem (lambda...

Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties. One...

_{a}^{b}{\frac {\partial }{\partial \alpha }}f(x,\alpha )\,dx.} By the Heine–Cantor theorem it is uniformly continuous in that set. In other words, for any ε...

properties which are not purely topological. On the other hand, the Heine–Cantor theorem states that if M1 is compact, then every continuous map is uniformly...

otherwise is continuous, and therefore uniformly continuous by the Heine-Cantor theorem. It does not satisfy a Hölder condition of any order, however. The...

space, Cantor's back-and-forth method, Cantor–Bernstein theorem, Heine–Cantor theorem Joseph Capgras, French psychologist – Capgras delusion Frank Capra...

theorem Goodstein's theorem Green's theorem (to do) Green's theorem when D is a simple region Heine–Borel theorem Intermediate value theorem Itô's lemma Kőnig's...

extreme value theorem, the Heine–Cantor theorem on uniform continuity, the Hahn–Banach theorem, and the Riemann mapping theorem. These theorems are analyzed...

Since it is also totally bounded, the Heine–Borel theorem says that it must be compact. For any point in the Cantor set and any arbitrarily small neighborhood...

of real numbers, thus it is uniformly continuous according to the Heine–Cantor theorem, so there is a positive real and monotonically non-decreasing function...

{1}{\infty }}.} ) Cauchy space – Concept in general topology and analysis Heine–Cantor theorem Eva Lowen-Colebunders (1989). Function Classes of Cauchy Continuous...

covers, the Heine-Borel property can be inferred. For every natural number n, the n-sphere is compact. Again from the Heine–Borel theorem, the closed...

Kossak), Eduard Heine, Georg Cantor, and Richard Dedekind was brought about. In 1869, Charles Méray had taken the same point of departure as Heine, but the theory...

(not necessarily Hausdorff) is balanced, which follows from the Heine–Cantor theorem for uniform spaces. Neither of these two sufficient conditions is...

Eduard Heine (Crelle's Journal, 74), Georg Cantor (Annalen, 5), and Richard Dedekind. Méray had taken in 1869 the same point of departure as Heine, but...

mathematician. In number theory, he proved special cases of Fermat's Last Theorem and created analytic number theory. In analysis, he advanced the theory...

interval is also an interval Heine–Borel theorem – sometimes used as the defining property of compactness Bolzano–Weierstrass theorem – states that each bounded...

category theorem Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's...

generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particular. This may also include the philosophical...

is complete and totally bounded. This is a generalization of the Heine–Borel theorem, which states that any closed and bounded subspace S {\displaystyle...

arguments cannot be removed. The following theorems are equivalent to Π1 1-CA0 over RCA0: The Cantor–Bendixson theorem (every closed set of reals is the union...