- #1

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- TL;DR Summary
- Trying to find a Formal Definition of the term.

Is it reasonable to define the n-dimensional holes of a topological space X as the non-zero Homology/Homotopy classes of X?

Can we read these as obstructions to continuously shrinking a simple closed curve * to a point within the space?

*I understand this is what we mean by a cycle.

Can we read these as obstructions to continuously shrinking a simple closed curve * to a point within the space?

*I understand this is what we mean by a cycle.