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Category of compactly generated weak Hausdorff spaces
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<p>In mathematics, the <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> of <a href="/facts/Compactly_generated_space/2A5umYGa">compactly generated</a> <a href="/facts/Weak_Hausdorff_space/2zl8Igzv">weak Hausdorff spaces</a>, CGWH, is a category used in <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a> as an alternative to the <a href="/facts/Category_of_topological_spaces/qH4SaEWa">category of topological spaces</a>, Top, as the latter lacks some properties that are common in practice and often convenient to use in proofs. There is also such a category for the CGWH analog of <a href="/facts/Pointed_space/V4DTgRCd">pointed topological spaces</a>, defined by requiring maps to preserve base points. </p><p>The articles <a href="/facts/Compactly_generated_space/2A5umYGa">compactly generated space</a> and <a href="/facts/Weak_Hausdorff_space/2zl8Igzv">weak Hausdorff space</a> define the respective topological properties. For the historical motivation behind these conditions on spaces, see <a href="/facts/Compactly_generated_space/2A5umYGa">Compactly generated space#Motivation</a>. This article focuses on the properties of the category. </p>