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Ambiguity in construction

[edit]

Section 2. Construction

 3. For each pair of identified points, choose a path in the disc joining these points, and construct a new disc with boundary this path. (So we add a disc for each pair of identified points.) 

A path between two points is a segment starting at one point, ending at the other. Boundary of a disc is homeomorphic with a circle. Could someone clarify how each new disc is constructed? lessismore (talk) 17:56, 17 October 2017 (UTC)[reply]