Non-CW Reeb spaces of continuous real-valued functions on nice Hausdorff spaces can be represented via simplified graphs, with concrete examples.
Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol
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Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.
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Representations of Reeb spaces via simplified graphs and examples
Non-CW Reeb spaces of continuous real-valued functions on nice Hausdorff spaces can be represented via simplified graphs, with concrete examples.
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Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles
Certain 3-manifolds are characterized by Morse functions with regular levels consisting only of spheres, tori, or Klein bottles.