Dimensions 0 and 1: Trivial
For more details on this topic, see Curve.There is a unique connected 0-dimensional manifold, namely the point, and disconnected 0-dimensional manifolds are just discrete sets, classified by cardinality. They have no geometry, and their study is combinatorics.
A connected 1-dimensional manifold without boundary is either the circle (if compact) or the real line (if not). However, maps of 1-dimensional manifolds are a non-trivial area; see below.
Read more about this topic: Classification Of Manifolds
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