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Topological entropy is one of the most difficult entropies to be used to analyze the DNA sequences, due to the finite sample and high-dimensionality problems. In order to overcome these problems, a generalized topological entropy is introduced. The relationship between the topological entropy and the generalized topological entropy is compared, which shows the topological entropy is a special case of the generalized entropy. As an application the generalized topological entropy in introns,doi:10.1371/journal.pone.0088519 pmid:24533097 pmcid:PMC3922877 fatcat:3n75oycpmzgktbl4jwof5se2ei