 In (Veldman 2011), equivalents of the fan principle over a basic theory called Basic Intuitionistic Mathematics are studied. It is shown that the fan principle is equivalent to the statement that the unit interval [0,1] has the Heine-Borel property, and from this many other equivalents are derived. In (Veldman 2009), the fan principle is shown to also be equivalent to Brouwer’s Approximate Fixed-Point Theorem. In (Lubarsky et al. 2012), reverse mathematics is applied to a form of Kripke’s schema, which is shown to be equivalent to certain topological statements.