منابع مشابه
Finite Dimensional Generating Spaces of Quasi-Norm Family
In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.
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The non-Hausdorff suspension of the one-sphere S1 of complex numbers fails to model the group’s continuous multiplication. Moreover, finite connected H-spaces are contractible, and therefore cannot model infinite connected non-contractible H-spaces. For an H-space and a finite model of the topology, the multiplication can be realized on the finite model after barycentric subdivision.
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Example 3. If X ⊆ RN is a vector space then it is a vector subspace of RN . Example 4. R1 is a vector subspace of R2. But the set [−1, 1] is not a vector subspace because it is not closed under either vector addition or scalar multiplication (for example, 1 + 1 = 2 6∈ [−1, 1]). Geometrically, a vector space in RN looks like a line, plane, or higher dimensional analog thereof, through the origin...
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Every ε-isometry u between real normed spaces of the same finite dimension which maps the origin to the origin may by uniformly approximated to within 2ε by a linear isometry. Under a smoothness hypothesis, necessary and sufficient conditions are obtained for the same conclusion to hold for a given ε-isometry between infinite-dimensional Banach spaces.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1971
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1971-12890-2