Coarse geometry deals with the large-scale geometry of a space as opposed to its small-scale structure. This paper investigates the concept of coarse geometry and specifically studies the coarse geometry of spaces regularly encountered in real analysis. We construct a non-separable space that is coarse equivalent to the separable space L1([a,b],m).

Author Bio

Phanuel Mariano is a 2012 graduate of Western Connecticut State University (WCSU) with a B.A. in mathematics, a minor in Finance and a graduate of the WCSU University Scholars Program. During his time at WCSU, he participated in various research groups, presented posters/talks three times at the annual AMS/MAA Joint Mathematics Meeting and gave a talk at the MAA Northeastern Section Spring Meeting. The research for this paper was conducted during the author's senior year at WCSU. The paper comprises of the author's senior undergraduate thesis. His current mathematical interests are in Probability Theory and Functional Analysis. His non-mathematical interests involve playing the drums, soccer, and listening to diverse types of music. In the fall of 2013, the author enrolled in the Ph.D. program in pure mathematics at the University of Connecticut.