Coronal mass ejections (CMEs) often exhibit the classic three-part structure in a coronagraph, i.e., the bright front, dark cavity, and bright core, which are traditionally considered as the manifestations of coronal plasma pileup, magnetic flux rope (MFR), and filament, respectively. However, a recent survey based on 42 CMEs all possessing the three-part structure found that a large majority (69%) do not contain an eruptive filament at the Sun. Therefore, a challenging opinion is proposed and

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... laims that the bright core can also correspond to the MFR, which is supported by the CME simulation. Then what is the nature of the CME core? In this paper, we address this issue through a CME associated with the eruption of a filament-hosting MFR on 2013 September 29. This CME exhibits the three-part morphology in multiple white-light coronagraphs from different perspectives. The new finding is that the bright core contains both a sharp and a fuzzy component. Through tracking the filament motion continuously from its source region to the outer corona, we conclude that the sharp component corresponds to the filament. The fuzzy component is suggested to result from the MFR that supports the filament against the gravity in the corona. Our study can shed more light on the nature of CME cores, and explain the core whether or not the filament is involved with a uniform scenario. The nature of the CME cavity is also discussed.