Results 1 to 10 of about 158,213 (204)
Infinite-Dimensional Manifolds as Ringed Spaces [PDF]
Publications of the Research Institute for Mathematical Sciences, 2017 We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces, and in terms ...
Michel Egeileh, Tilmann Wurzbacher
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Triangulated infinite-dimensional manifolds [PDF]
Bulletin of the American Mathematical Society, 1970 In this paper we extend almost all the results on infinite-dimensional Fréchet manifolds to apply to manifolds modeled on some 2̂ ( = {#£^1 at most finitely many of the coordinates of x are nonzero } ) and we show (Theorem 14) that each /^-manifold has a
David W. Henderson, James E. West
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Infinite-dimensional manifolds related to C-spaces
Pracì Mìžnarodnogo Geometričnogo Centru, 2020 Haver's property C turns out to be related to Borst's transfinite extension of the covering dimension. We prove that, for a uncountably many countable ordinals β there exists a strongly universal kω-space for the class of spaces of transfinite covering ...
Mykhailo Zarichnyi, Oryslava Polivoda
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Fixed point theorems on infinite dimensional manifolds [PDF]
Transactions of the American Mathematical Society, 1965 Introduction. Let X be a differentiable manifold of finite or infinite dimension, f a continuous mapping of X into X. f is said to be a compact mapping if f(X) is relatively compact in X while f is said to be locally compact if each point x of X has a neighborhood Nx such that f(Nx) is relatively compact in X. We are concerned in the present paper with
Felix E. Browder
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Factors of Infinite-Dimensional Manifolds [PDF]
Transactions of the American Mathematical Society, 1969 R. D. Anderson, R. Schori
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On Infinite-Dimensional Manifold Triples [PDF]
Transactions of the American Mathematical Society, 1990 Let Q Q denote the Hilbert cube [ − 1 , 1 ] ω , s = ( − 1 , 1 ) ω {[ - 1,1]^\omega },\;s = {( - 1,1)^\omega }
Katsuro Sakai, Raymond Y. T. Wong
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Some applications of transversality for infinite dimensional manifolds
Pracì Mìžnarodnogo Geometričnogo Centru, 2021 We present some transversality results for a category of Frechet manifolds, the so-called MCk - Frechet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we ...
Kaveh Eftekharinasab
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Integration theory on infinite-dimensional manifolds [PDF]
Transactions of the American Mathematical Society, 1971 The purpose of this paper is to develop a natural integration theory over a suitable kind of infinite-dimensional manifold. The type of manifold we study is a curved analogue of an abstract Wiener space. Let H H be a real separable Hilbert space, B B the completion of H H with respect to a ...
H. Kuo
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Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions [PDF]
, 2014 We introduce a notion of a weak Poisson structure on a manifold M modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra \(\mathcal{A}\subseteq C^{\infty }(M)\) which has to satisfy a non-degeneracy condition (the
Karl‐Hermann Neeb +2 more
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Sub-Riemannian Geometry on Infinite-Dimensional Manifolds [PDF]
The Journal of Geometric Analysis, 2012 We generalize the concept of sub-Riemannian geometry to infinite-dimensional manifolds modeled on convenient vector spaces. On a sub-Riemannian manifold $$M$$M, the metric is defined only on a sub-bundle $${{\mathrm{\mathcal {H}}}}$$H of the tangent ...
E. Grong, I. Markina, A. Vasil’ev
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