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I just learned in my textbook about point open topology. My question is: What is the difference between point open topology (also known as the topology of pointwise convergence) and product topology since they are both defined by continuous projections? Can you explain to me the difference and give me an example?

yoyo
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    You will need to define "point open topology" for us. It does not seem to be standard terminology, Perhaps it was something unique to that textbook. – GEdgar Dec 31 '20 at 12:54
  • I edited the question. I checked online and it seems that it is also called topology of pointwise convergence. – yoyo Dec 31 '20 at 13:36
  • It is basically the same thing, but "topology of pointwise convergence" is used for any subspace of the product. – Captain Lama Dec 31 '20 at 15:02
  • Is it give answer of your question ? https://math.stackexchange.com/questions/2208634/pointwise-convergence-and-convergence-in-product-topology – nmasanta Dec 31 '20 at 15:12
  • possible duplicate https://math.stackexchange.com/q/411045 – Mirko Jan 01 '21 at 03:20
  • @Mirko Yes, thank you! – yoyo Jan 02 '21 at 17:15

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