Near-continuous functions and near-continuous homotopy

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Ronnie Christian Goolsby (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: The purpose of this thesis is to investigate and study the ideas of near-continuous functions and near-continuous homotopy. The ideas of near-continuous functions and near-continuous homotopy originated in [3] and [4]. The reader is expected to have a knowledge of point set topology, and is referred to [1] for definitions and results not given in this thesis. In Chapter 1, near-continuous is defined and relationships between near-continuous and continuous functions are proved. Surprisingly, a characterization of T1 - spaces also arises. In Chapter 2, certain topological properties which are preserved by continuous functions are seen to be preserved by near-continuous functions. It is also shown that, although separable is preserved under continuous functions, separable is not preserved under near-continuous functions. In Chapter 3, near-continuous retracts and near-continuous fixed points are defined and studied. In Chapter 4, the near-continuous fundamental group is defined, and although the proofs of theorems turn out by necessity to be different, the usual theorems about fundamental groups are proved. In Chapter 5, examples are proved to show that the near-continuous fundamental group is non-trivial and different from the fundamental group.

Additional Information

Language: English
Date: 1972
Functions, Continuous
Homotopy theory

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