Solve a Graph theory problem using Topology | Bruijn Erdos Theorem

Bruijn Erdos Theorem states thats if any subgraph of an infinite graph is k colorable, the graph itself is k colorable. Tychonoff's theorem can help us in proving the theorem which states that an arbitrary product of compact sets is compact.

[subhradipgiri]

You're doing a great job brother... India needs more youtubers like you. Carry on. We want more frequent videos from you.
Soliderity from mathematical fraternity ✊

[souvikpatrahowrah]

Production quality increase appreciated 👍

[yogiaditynathji]

अद्भूत वीडियो । आपकी यह वीडियो देखकर बहुत प्रसन्नता हुई ।
आपके भविश्य के लिये शुभकामनाएं ।

जय श्री राम ।

[uddalakmukherjee]

Thats why he is the GOAT, the GOAT 🐐🐐🔥🔥🔥 On a serious note, this is something I've never encountered before, and I think the catch is to understand how the basic open sets are defined in correlation with the actual definition of the basis of a product topology and also understanding the graph theoritic interpretation of the open sets as well as their finite intersection. Also the fact that the union of the basic sets are clopen is quite essential for the closure of the proof where we used the finite intersection property. The rest is pretty easy to follow, I was thinking if this proof could be simplified with the use of G delta and F sigma sets since in the end we are working with the intersection of union of base elements of a topology 😃 Nevertheless what a banger of a video 🔥🔥🔥🔥

[adityaujjwal]

Maybe make a series of videos on some topic like ODEs and PDEs with visualisation?

[ethanbottomley-mason]

The actual statement of the theorem sounds like the compactness theorem for first order logic. Is this not just a simple consequence of the compactness theorem?