Manifolds with varying (local or global) dimension

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What subject should one look into to understand manifolds with varying dimensions throughout it's structure.

For example, Imagine a 2-sphere with a line going through it defining some type of manifold, could we still consider that as a manifold? Or is it another type of geometric object.(non-'Pure' Mani,,,?<--I need something better than this).

Anyone who has any resources on differential geometries with non-constant dimensions please leave as an answer (I have university resources so feel free to offer 'subscription based' services).