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Reference.org
Mapping space
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<p>In mathematics, especially in <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a>, the mapping space between two spaces is the space of all the (continuous) maps between them. </p><p>Viewing the set of all the maps as a space is useful because that allows for topological considerations. For example, a curve h : I → Map ( X , Y ) {\displaystyle h:I\to \operatorname {Map} (X,Y)} in the mapping space is exactly a <a href="/facts/Homotopy/1nWrPxdj">homotopy</a>. </p>