# Homotopy of compact non-orientable surfaces

From Topospaces

This article describes the value (and the process used to compute it) of some homotopy invariant(s) for a topological space or family of topological spaces. The invariant is homotopy and the topological space/family is compact non-orientable surface

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## Statement

This article describes the homotopy groups, including the set of path components , the fundamental group , and the higher homotopy groups of the compact non-orientable surface , which is defined as the connected sum of copies of the real projective plane .

### Set of path components

Each of the spaces is a path-connected space, so its set of path components is a one-point space.

### Fundamental group

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