Topologies and smooth structures on initial and final objects in the category of frolicher spaces - Mahudu, Ben Moditi (My University, 2019)
The 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 algorithmic
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulﬁllment of the requirements for the degree of Master of Science. Johannesburg, 2019