Ep. 1 Introduction: Navigating Metric Space Topology

This is the start of a new series that will roughly cover just enough topics in metric space topology to set a foundation for many disciplines in college-level mathematics, like real/complex analysis. In this video, I give a rough pictorial intuition for the term "metric space topology" and a couple of concepts (namely, homeomorphism and compactness) that we will examine more closely later in the series.

I take time here to express my wholehearted gratitude to my professors and friends from college, my family, and various authors of topology and analysis textbooks I've explored, who made this series a reality. In particular, some of these authors deserve to be included as references for this metric space topology series, as done so below; I highly encourage you to check out some of them. If I make references of the form "[author's name]" in this series, the textbook I'm referring to is the one provided below.

[Abbott] Stephen Abbott's "Understanding Analysis"
[Lang] Serge Lang's "Undergraduate Analysis"
[Munkres] James Munkres's "Topology"
[Pugh] Charles Pugh's "Real Mathematical Analysis"
[Rudin] Walter Rudin's "Principles of Mathematical Analysis"

I add that matplotlib and numpy were used in making some of the graphs, examples, and problems.

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Any likes, shares, comments, and constructive criticisms are much appreciated.

[mihirvora]

Fascinating, I feel like this is going to be an interesting series!

[pra.]

loving the undergraduate level content!

[pichass]

Nice! I always love seeing new covers of Baby Rudin

[motherflerkentannhauser]

In my opinion and experience, studying point-set topology first in which metric topology is introduced as an example is much more systematic. If this is my first time with topology, I'd find it just as confusing as those "donuts homeomorphic to coffee mugs" introductions, which is in fact algebraic topology (fundamental groups & Euler characteristics), something you don't engage in before fully digesting the first 4 chapters of Munkres.