Metric Spaces 2: Open Sets

Presented by Dr. Joon Kang on Sept 6, 2022.

[theklausjesper]

This feels like combining the relaxing parts of asmr and the stress that I need to know this before my exam. 10/10

[hamc]

Euclidean spaces have n points represented by real numbers (x1, x2, ..., xn) and a dot product whereas the continuous function example is completely different but we can still find a notion of a distance function and hence a metric space which isnt just points in n-dimensional space. The example is to show its not just a concept that applies to euclidean spaces.

[vaishnavikumar]

Please upload the course website and all videos regarding it

[filmmyduniya-mfhq]

Can i use max instead of sup bcz the image set is closed and bounded.

[afoster]

First, let me say I enjoyed the video! I did get that C([a, b]) equipped with d(f, g) = | f(x) - g(x)| for all x in [a, b] is a Metric Space and (R^n, d^*) where d^* is the standard metric are metric spaces. But I'm confused as to how is (C([a, b]), d) is a non-euclidean metric space and (R^n, d^*) is euclidean? I didn't see you provide any definitions of what a Euclidean Metric Space is (if there is such a thing). I guess my question is What makes a space Euclidean as opposed to non-euclidean? Nevertheless, a great job!