In topology, the pasting or gluing lemma, and sometimes the gluing rule, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions. For example, in the book Topology and Groupoids, where the condition given for the statement below is that and The pasting lemma is crucial to the construction of the fundamental group or fundamental groupoid of a topological space; it allows one to concatenate continuous paths to create a new continuous path.
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| - Verklebungslemma (de)
- Pasting lemma (en)
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| - Das Verklebungslemma (englisch glueing lemma bzw. gluing lemma oder pasting lemma) ist ein elementarer Lehrsatz des mathematischen Teilgebiets der Allgemeinen Topologie. Es zeigt, wie unter gewissen Bedingungen stetige Abbildungen auf topologischer Räumen aus solchen auf Unterräumen stückweise zusammengefügt und damit gewissermaßen „zusammengeklebt“ werden können. (de)
- In topology, the pasting or gluing lemma, and sometimes the gluing rule, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions. For example, in the book Topology and Groupoids, where the condition given for the statement below is that and The pasting lemma is crucial to the construction of the fundamental group or fundamental groupoid of a topological space; it allows one to concatenate continuous paths to create a new continuous path. (en)
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| - Das Verklebungslemma (englisch glueing lemma bzw. gluing lemma oder pasting lemma) ist ein elementarer Lehrsatz des mathematischen Teilgebiets der Allgemeinen Topologie. Es zeigt, wie unter gewissen Bedingungen stetige Abbildungen auf topologischer Räumen aus solchen auf Unterräumen stückweise zusammengefügt und damit gewissermaßen „zusammengeklebt“ werden können. (de)
- In topology, the pasting or gluing lemma, and sometimes the gluing rule, is an important result which says that two continuous functions can be "glued together" to create another continuous function. The lemma is implicit in the use of piecewise functions. For example, in the book Topology and Groupoids, where the condition given for the statement below is that and The pasting lemma is crucial to the construction of the fundamental group or fundamental groupoid of a topological space; it allows one to concatenate continuous paths to create a new continuous path. (en)
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