Document Type

Honors Thesis


The field of topology is concerned with the study of “topological spaces,” mathematical objects used to describe space and change at their most fundamental levels. Within this thesis, a study of a class of topological spaces, called partition spaces, is conducted. Four results concerning such spaces are presented, together with formal proofs and illustrative examples. The first result describes the behavior of limits of sequences in partition spaces. The second result characterizes continuous functions between such spaces. From the first and second results, a third finding is derived that relates continuous functions between partition spaces to limits of sequences in their domains. Lastly, the fourth result establishes necessary and sufficient conditions for a function between partition spaces to be a homeomorphism. These results are not found explicitly within the mathematical literature and are self-contained in their development. Together, they comprise a basic description of continuous functions between partition spaces.

Publication Date






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