Open Mapping Theorem
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Open Mapping Theorem

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, there are two theorems with the name "open mapping theorem". In both cases, they give conditions under which certain maps are open maps, i.e. they map open sets to open sets. They are significant results in their respective contexts since, unlike inverse images, direct images of functions are much less tractable in general. In functional analysis, the open mapping theorem or Banach Schauder theorem states that a surjective continuous linear transformat...