Abstract
A spectral sequence is defined for a closed map of finite multiplicity which coincides with the Cartan-Grothendieck spectral sequence in the case of a map onto a quotient space by a finite group acting freely [1, 2]. It is proved that the resolution by means of which the spectral sequence is defined can be described within the framework of the so-called theory of triples. A definition of this sequence is given for an arbitrary continuous map. It is shown that the spectral sequences of coverings are the spectral sequences of special continuous maps.
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Translated from Matematicheskie Zametki, Vol. 23, No. 3, pp. 435–446, March, 1978.
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Zarelua, A.V. A spectral sequence associated with a continuous map. Mathematical Notes of the Academy of Sciences of the USSR 23, 236–241 (1978). https://doi.org/10.1007/BF01651439
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DOI: https://doi.org/10.1007/BF01651439