in Morse theory,
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Topology on L a, b : Fix a broken λ λ , ... , λ . Its neighborhood consists of its deformations and smoothings. Key: every smooth trajectory has R symmetry. Can reduce to a level set in a Morse chart to see all its small deformations! Base of open sets: W λ, U , U where U consists of a neighborhood of the exit point of λ in a Morse chart of each broken point; similarly U consists of neighborhoods of entry points; W λ, U , U consists of broken trajectories whose broken points are subset of that of λ, and whose exit and entry points 3. Morse complex