In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms...

the Poincaré conjecture, correcting an error in an earlier paper Whitehead (1934, theorem 3) where he incorrectly claimed that no such manifold exists. A...

John Henry Constantine Whitehead FRS (11 November 1904 – 8 May 1960), known as "Henry", was a British mathematician and was one of the founders of homotopy...

fixed-point theorem Leray–Hirsch theorem Poincaré duality theorem Seifert–van Kampen theorem Universal coefficient theorem Whitehead theorem Algebraic K-theory...

groups of spheres Plus construction Whitehead theorem Weak equivalence Hurewicz theorem H-space Künneth theorem De Rham cohomology Obstruction theory...

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving...

homotopy-theoretic pathologies of arbitrary topological spaces. For example, the Whitehead theorem holds for ANRs: a map of ANRs that induces an isomorphism on homotopy...

Alfred North Whitehead OM FRS FBA (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school...

always contained in a finite subcomplex. CW complexes satisfy the Whitehead theorem: a map between CW complexes is a homotopy equivalence if and only...

(mathematical logic) Whitehead theorem (homotopy theory) Whitney embedding theorem (differential manifolds) Whitney extension theorem (mathematical analysis)...

_{1}(A\cap B)} and the generalised Whitehead products. The proof of this theorem uses a higher homotopy van Kampen type theorem for triadic homotopy groups,...

the s-cobordism theorem states that if the manifolds are not simply-connected, an h-cobordism is a cylinder if and only if the Whitehead torsion of the...

cofibration. Hovey (1999), Definition 2.4.3. Hatcher (2002), Theorem 4.32. Is there the Whitehead theorem for cohomology theory? Strøm (1972). Beke (2000), Proposition...

In mathematics, the Gordon–Luecke theorem on knot complements states that if the complements of two tame knots are homeomorphic, then the knots are equivalent...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

contractible if all of its homotopy groups are trivial. It follows from Whitehead's Theorem that if a CW-complex is weakly contractible then it is contractible...

However these two spaces are not homotopy equivalent. So by the Whitehead theorem, the Warsaw circle does not have the homotopy type of a CW complex...

incompleteness theorem of 1931, previous examples of undecidable statements (such as the continuum hypothesis) had all been in pure set theory. The Whitehead problem...

then X is a contractible space, as follows from the Whitehead theorem and the Hurewicz theorem. Acyclic spaces occur in topology, where they can be used...

structures — they are uniquely triangulizable, by Whitehead's theorem on triangulation (Whitehead 1940) — but PL manifolds do not always have smooth...

h-cobordism theorem because the simple connectedness hypotheses imply that the relevant Whitehead group is trivial. In fact the s-cobordism theorem implies...

is exactly the Whitehead torsion τ (W, M) of the inclusion M ↪ W {\displaystyle M\hookrightarrow W} . Precisely, the s-cobordism theorem (the s stands...

yα. Since B is assumed to support a C∞ structure, according to the Whitehead theorem one can fix a Riemannian metric on B and choose the atlas U {\displaystyle...

contractible. Indeed, contractibility of a universal cover is the same, by Whitehead's theorem, as asphericality of it. And it is an application of the exact sequence...

are abelian. Universal coefficient theorem Dold–Thom theorem See also: Characteristic class, Postnikov tower, Whitehead torsion There are several specific...

Cambridge University Press, ISBN 0-521-79540-0. Whitehead, G. W. (1953), "On the Freudenthal Theorems", Annals of Mathematics, 57 (2): 209–228, doi:10...

computational demonstration of theorems in PM Introduction to Mathematical Philosophy Hardy 2004, p. 83. Littlewood 1986, p. 130. Whitehead, Alfred North; Russell...

intuitionistic logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica as: ∗ 4 ⋅ 13 .     ⊢ ...

intelligence program". Logic Theorist proved 38 of the first 52 theorems in chapter two of Whitehead and Bertrand Russell's Principia Mathematica, and found new...

term. This result was later generalized by Rice's theorem. In 1973, Saharon Shelah showed the Whitehead problem in group theory is undecidable, in the first...