Mahudu, Ben Moditi2019-09-062019-09-062019https://hdl.handle.net/10539/28048A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science. Johannesburg, 2019The initial objects (in the category of Fro¨licher spaces) being studied are Fro¨licher subspace, product and equalizer’s domain; and the final objects are Fro¨licher quotient, coproduct and coequalizer’s codomain. For each object a canonical topology (from the category of topologies) is induced on the underlying set of the object, and Fro¨licher topologies are induced from the Fr¨olicher structure. There are two Fr¨olicher topologies for each object: a Fro¨licher topology induced from structure curves and a Fr¨olicher topology induced from structure functions - it’s shown that the former Fr¨olicher topology is finer than the latter Fr¨olicher topology for any Fr¨olicher space. It’s shown that for each initial object the canonical topology is coarser than the Fro¨licher topology induced from structure functions, and for each final object the canonical topology is finer than the Fr¨olicher topology induced from structure curves. Furthermore we establish that the building structure for each object is constant and algorithmicenThesis