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We study the thermodynamic properties and critical behaviors of the topological charged black hole in AdS space under the consideration of the generalized uncertainty principle (GUP). It is found that only in the spherical horizon case there are Van der Waals-like first-order phase transitions and reentrant phase transitions. From the equation of state we find that the GUP-corrected black hole can have one, two, and three apparent critical points under different conditions. However, it isdoi:10.1155/2018/1257631 fatcat:ez3iqkdcmvggzdbgvmrgrrv634