TY - JOUR
AU - Rogers, Ryan Joseph
AU - Zhong, Ning
PY - 2019/08/01
Y2 - 2024/11/08
TI - From Euclidean Spaces to Metric Spaces
JF - Journal of Student Research
JA - J Stud Res
VL - 8
IS - 1
SE -
DO - 10.47611/jsr.v8i1.472
UR - https://www.jsr.org/index.php/path/article/view/472
SP -
AB - <p>In this note, we provide the definition of a metric space and establish that, while all Euclidean spaces are metric spaces, not all metric spaces are Euclidean spaces. It is then natural and interesting to ask which theorems that hold in Euclidean spaces can be extended to general metric spaces and which ones cannot be extended. We survey this topic by considering six well-known theorems which hold in Euclidean spaces and rigorously exploring their validities in general metric spaces.</p>
ER -