| 11. | This is now called the Brown Gersten spectral sequence.
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| 12. | A very common type of spectral sequence comes from a filtered cochain complex.
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| 13. | To get a spectral sequence, we will reduce to the previous example.
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| 14. | This is the content of the Adams spectral sequence.
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| 15. | For a basic example, see Bockstein spectral sequence.
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| 16. | Zigzag persistence may turn out to be of theoretical importance to spectral sequences.
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| 17. | In other words, the spectral sequence should satisfy
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| 18. | Then there is a spectral sequence of cohomological type
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| 19. | It is evident to mathematicians that persistent homology is closely related to spectral sequences.
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| 20. | This follows from the Atiyah Hirzebruch spectral sequence.
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