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We prove that each non-separable completely metrizable convex subset of a Fréchet space is homeomorphic to a Hilbert space. This resolves a more than 30 years old problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowolski and Toruńczyk, this result implies that each closed convex subset of a Fréchet space is homeomorphic to $[0, 1] ⁿ \times {[0, 1)}^{m} \times ℓ ₂ (κ)$ for some cardinals 0 ≤ n ≤ ω, 0 ≤ m ≤ 1 and κ ≥ 0.

Topological classification of conformal actions on $p q$ -hyperelliptic Riemann surfaces.

Tyszkowska, Ewa (2007)

International Journal of Mathematics and Mathematical Sciences

Topological classification of multiaxial $U (n)$ -actions (with an appendix by Jared Bass)

Sylvain Cappell, Shmuel Weinberger, Min Yan (2015)

Journal of the European Mathematical Society

This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological...

Topological classification of strong duals to nuclear (LF)-spaces

Taras Banakh (2000)

Studia Mathematica

We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^{ω}$ , $ℝ^{\infty}$ , $Q \times ℝ^{\infty}$ , $ℝ^{ω} \times ℝ^{\infty}$ , or ${(ℝ^{\infty})}^{ω}$ , where $ℝ^{\infty} = l i m ℝ^{n}$ and $Q = {[- 1, 1]}^{ω}$ . In particular, the Schwartz space D’ of distributions is homeomorphic to ${(ℝ^{\infty})}^{ω}$ . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic either...

Topological components of spaces of representations.

William M. Goldman (1988)

Inventiones mathematicae

Topological conjugacy of locally free $𝐑^{n - 1}$ actions on $n$ -manifolds

David C. Tischler, Rosamond W. Tischler (1974)

Annales de l'institut Fourier

For actions as in the title we associate a collection of rotation numbers. If one of them is sufficiently irrational then the action is conjugate (as an action) to either a linear action on a torus or to an action on a principal $T^{k}$ bundle over $T^{2}$ with $T^{k} \times R^{1}$ orbits.

Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)

Enhui Shi, Lizhen Zhou (2016)

Colloquium Mathematicae

Let ℝ be the real line and let Homeo₊(ℝ) be the orientation preserving homeomorphism group of ℝ. Then a subgroup G of Homeo₊(ℝ) is called tightly transitive if there is some point x ∈ X such that the orbit Gx is dense in X and no subgroups H of G with |G:H| = ∞ have this property. In this paper, for each integer n > 1, we determine all the topological conjugation classes of tightly transitive subgroups G of Homeo₊(ℝ) which are isomorphic to ℤⁿ and have countably many nontransitive points.

Topological geodesics and virtual rigidity.

Funar, Louis, Gadgil, Siddhartha (2001)

Algebraic & Geometric Topology

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Taras Banakh, Igor Zarichnyy (2008)

Open Mathematics

Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover $𝒰$ of X there is a sequence of maps (f n: X → X)nεgw such that each f n is $𝒰$ -near to the identity map of X and the family f n(X)n∈ω is locally finite...

Topological manifolds and real algebraic geometry

Alberto Tognoli (2003)

Bollettino dell'Unione Matematica Italiana

We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological $4$ -manifolds.

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To the question about the maximum principle for manifolds over local algebras.

Topología grassmaniana sobre los ideales cerrados de codimensión finita de un álgebra de Banach conmutativa.

Topological charges and high dimensional instantons

Topological Classification and Bifurcations of Holomorphic Flows with Resonances in ...2.

Topological Classification of 4-Dimensional Complete Intersections.

Topological classification of closed convex sets in Fréchet spaces

Topological classification of conformal actions on $p q$ -hyperelliptic Riemann surfaces.

Topological classification of multiaxial $U (n)$ -actions (with an appendix by Jared Bass)

Topological classification of strong duals to nuclear (LF)-spaces

Topological components of spaces of representations.

Topological conjugacy of locally free $𝐑^{n - 1}$ actions on $n$ -manifolds

Topological conjugation classes of tightly transitive subgroups of Homeo₊(ℝ)

Topological geodesics and virtual rigidity.

Topological groups and convex sets homeomorphic to non-separable Hilbert spaces

Topological manifolds and real algebraic geometry

Topological Order Complexes and Resolutions of Discriminant Sets

Topological order complexes and resolutions of discriminant sets.

Topological properties of high-dimensional handles

Topological quantum field theory

Topological stability for infinite-dimensional manifolds

Currently displaying 421 – 440 of 558