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... homeomorphic to its unit sphere S [14, 3]. A key ingredient of the proof is the topological equivalence L ' L × R for every infinite-dimensional Banach space L. The assertion will follow from this since S is homeomorphic to an (infinite-dimensional) closed hyperplane L of E which is in turn homeomor ...
... homeomorphic to its unit sphere S [14, 3]. A key ingredient of the proof is the topological equivalence L ' L × R for every infinite-dimensional Banach space L. The assertion will follow from this since S is homeomorphic to an (infinite-dimensional) closed hyperplane L of E which is in turn homeomor ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.