  Fan-spine is a special topology in solar atmosphere and is closely related to
magnetic null point as well as circular-ribbon flares, which can provide
important information for understanding the intrinsic three-dimensional (3D)
nature of solar flares. However, the fine structure within the fan has rarely
been investigated. In present paper, we investigate a secondary fan-spine (SFS)
structure within the fan of a larger fan-spine topology. On 2013 November 18,
this large fan-spine structure was traced out due to the partial eruption of a
filament, which caused a circular-ribbon flare in active region 11897. The
extrapolated 3D magnetic fields and squashing factor Q maps depict distinctly
this fan-spine topology, its surrounding quasi-separatrix layer (QSL) halo, and
a smaller quasi-circular ribbon with high Q located in the center, which
implies the existence of fine structure within the fan. The imaging
observations, extrapolated 3D fields, and Q maps on November 17 show that there
indeed exists an SFS surrounded by a QSL, which is enveloped by another
QSL-halo corresponding to the overlying larger domeshaped fan. Moreover, the
material flows caused by the null-point reconnection are also detected along
this SFS. After checking the evolution of the underneath magnetic fields, we
suggest that the continuous emergence of magnetic flux within the central
parasitic region encompassed by the opposite-polarity fields results in the
formation of the SFS under the large fan.
