| dbo:abstract |
In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article discusses topologies on such spaces in the more general setting of topological vector spaces (TVSs). (en) 해석학에서 균등 수렴 위상(均等收斂位相, 영어: topology of uniform convergence)은 일반위상수학적인 극한이 균등 수렴과 일치하게 하는, 함수 공간 위의 위상이다. 이 경우, 공역에 위상 벡터 공간 또는 (보다 일반적으로) 균등 공간 구조가 필요하다. 만약 공역에 거리 공간이나 노름 공간과 같은 구조가 주어지면, 이 위상 및 균등 공간 구조와 호환되는 균등 거리 함수(영어: uniform metric) 및 균등 노름(영어: uniform norm)을 정의할 수 있다. (ko) |
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| dbp:mathStatement |
Let be a non-empty collection of bounded subsets of Then the -topology on is not altered if is replaced by any of the following collections of subsets of : all subsets of all finite unions of sets in ; all scalar multiples of all sets in ; all finite Minkowski sums of sets in ; the balanced hull of every set in ; the closure of every set in ; and if and are locally convex, then we may add to this list: the closed convex balanced hull of every set in (en) If and if is a net in then in the -topology on if and only if for every converges uniformly to on (en) The -topology on is compatible with the vector space structure of if and only if every is -bounded; that is, if and only if for every and every is bounded in (en) |
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Theorem (en) |
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In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article discusses topologies on such spaces in the more general setting of topological vector spaces (TVSs). (en) 해석학에서 균등 수렴 위상(均等收斂位相, 영어: topology of uniform convergence)은 일반위상수학적인 극한이 균등 수렴과 일치하게 하는, 함수 공간 위의 위상이다. 이 경우, 공역에 위상 벡터 공간 또는 (보다 일반적으로) 균등 공간 구조가 필요하다. 만약 공역에 거리 공간이나 노름 공간과 같은 구조가 주어지면, 이 위상 및 균등 공간 구조와 호환되는 균등 거리 함수(영어: uniform metric) 및 균등 노름(영어: uniform norm)을 정의할 수 있다. (ko) |
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균등 수렴 위상 (ko) Topologies on spaces of linear maps (en) |
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