Open mapping theorem
Open mapping theorem In mathematics, there are two theorems with the name "open mapping theorem". Functional analysis In functional analysis, ...
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Riemann mapping theorem   (translated from German)
Riemann mapping theorem That (small) Riemann mapping theorem (after Bernhard Riemann ) from the year 1851 ... clarifying the terms used in this sentence: (open) the unit circular disk (the open ...
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Riemann mapping theorem
Riemann mapping theorem In complex analysis, the Riemann mapping theorem, named after Bernhard Riemann, states the following: if U is a simply connected open subset of the complex number plane ...
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Carathéodory's theorem (conformal mapping)
Carathéodory's theorem (conformal mapping) See also Carathéodory's theorem for other meanings. In mathematics, Carathéodory's theorem in complex analysis states that if U is a simply connected open subset of the complex plane C, ...
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Continuous mapping   (translated from Russian)
Continuous mapping In to mathematics the mapping or the function it is called continuous ... in the section), they are characterized by theorem Bol'tsano - Cauchy and by the Weyerstrass theorem. If the function not of nepreryna at ... f(.a)\| &.lt; \.varepsilon)&.lt;/.matyu&.gt; Mapping the metric spaces In the previous ...
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Riesz representation theorem
Riesz representation theorem There are several well-known theorems in ... functional analysis known as the Riesz representation theorem. The Hilbert space representation theorem This theorem establishes an important connection between a Hilbert ... an element of H '. The Riesz representation theorem states that every element of H ' ...
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Baire category theorem
Baire category theorem The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives ... be a Baire space. Statement of the theorem (BCT1) Every non-empty complete metric space ... topological space which is homeomorphic to an open subset of a complete pseudometric space ...
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Jordan curved line theorem   (translated from Japanese)
Jordan curved line theorem topology ,Jordan curved line theorem(Jordan sewer habit it is - the て to need,Jordan curve theorem) Or JordanClosed curve theorem(Fence sewer habit it is the て ... is formed. Contents of Jordan curved line theorem are thought, like glance clear thing, ...
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Open and closed maps
Open and closed maps In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X → Y is open if for any open set U ...
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Theorem of median value   (translated from Japanese)
Theorem of median value Theorem of median value(The て of the ... Below regarding connectivity, the way existence type Theorem So it is: TruthNumber line R Closed ... connection Topological space The image by continual mapping quickly it is beam connection) from it is the theorem which consists. Proof Only outline expresses. ...
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