For a given category, these objects name an equivalent subcategory where no two distinct objects are isomorphic. For 10 points each:
[10h] Identify these objects, which name the constituent spaces of the sequence of topological spaces defining a CW complex.
ANSWER: skeletons [accept skeletal category; accept skeleta; accept k or n-skeletons]
[10m] Real examples of one of these spaces admit a CW complex structure where lower dimensional examples of these spaces make up each k-skeleton of the complex. The Fano plane is the smallest finite example of a 2-dimensional example of these spaces.
ANSWER: projective spaces [accept projective planes or projective lines]
[10e] This shape exemplifies a one-dimensional CW complex because it consists of a single point attached to the unit 1-ball at both ends. In the complex plane, this shape is traced out by the points e to the i theta.
ANSWER: circle [accept S1 or 1-sphere; reject “1-ball”]
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