Abstract
This paper is concerned with some topological properties of a notion of distance between normed linear spaces which is due to Banach and Mazur [1], We are interested in a pseudometric space associated naturally with this notion of distance, and our main result is that this pseudometric space is always pathwise connected.
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The results in this paper were taken from the author's doctoral dissertation written at the University of Maryland under the direction of Robert Whitley. The research was partially supported by the N.S.F.
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McGuigan, R.A. On the connectedness of isomorphism classes. Manuscripta Math 3, 1–5 (1970). https://doi.org/10.1007/BF01168459
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DOI: https://doi.org/10.1007/BF01168459