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Haynes Robert Miller (born January 29, 1948, in Princeton, New Jersey) [1] is an American mathematician specializing in algebraic topology.. Miller completed his undergraduate study at Harvard University and earned his PhD in 1974 under the supervision of John Coleman Moore at Princeton University with thesis Some Algebraic Aspects of the Adams–Novikov Spectral Sequence. [2]
Miller's theorem generalizes to a version of Sullivan's conjecture in which the action on is allowed to be non-trivial. In, [ 3 ] Sullivan conjectured that η is a weak equivalence after a certain p-completion procedure due to A. Bousfield and D. Kan for the group G = Z / 2 {\displaystyle G=Z/2} .
Trivial topology; Cofinite topology; Finer topology; Product topology. Restricted product; Quotient space; Unit interval; Continuum (topology) Extended real number line; Long line (topology) Sierpinski space; Cantor set, Cantor space, Cantor cube; Space-filling curve; Topologist's sine curve; Uniform norm; Weak topology; Strong topology ...
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism , though usually most classify up to homotopy equivalence .
Steenrod algebra; Bott periodicity theorem; K-theory. Topological K-theory; Adams operation; Algebraic K-theory; Whitehead torsion; Twisted K-theory; Cobordism; Thom space; Suspension functor; Stable homotopy theory; Spectrum (homotopy theory) Morava K-theory; Hodge conjecture; Weil conjectures; Directed algebraic topology
Haynes Miller: Sullivan conjecture: classifying spaces: Miller proved the version on mapping BG to a finite complex. 1987: Grigory Margulis: Oppenheim conjecture: diophantine approximation: Margulis proved the conjecture with ergodic theory methods. 1989: Vladimir I. Chernousov: Weil's conjecture on Tamagawa numbers: algebraic groups
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property .
Absolutely closed See H-closed Accessible See . Accumulation point See limit point. Alexandrov topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently, if arbitrary unions of closed sets are closed, or, again equivalently, if the open sets are the upper sets of a poset.