Density Results in C(Sn; Sn) for Lower Dimensions and Riemannian Morphisms
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A standard paradigm in the expansion of knowledge is to describe nearby familiar objects of a new object. Density results in topology may be viewed as tting into this paradigm. Another such paradigm is to give relations between new and relatively familiar objects. Morphisms between objects of a category may be viewed as falling under this paradigm. In this thesis, we have considered problems from these two paradigms. We have studied density results in the spaces of continuous functions C(S1; S1) and C(S2; S2). In the second half of the thesis we have de ned and explored morphisms between Riemannian manifolds.
Supervisor: K.V. Srikanth