# What is the closure of the set of continuous bounded real valued functions on $\mathbb{R}^d$ under pointwise convergence?

What is the closure of the set of continuous bounded real-valued functions on $$\mathbb{R}^d$$ under pointwise convergence? How might one go about finding this closure? Also, are there common names for spaces of functions equipped with different notions of convergence (topologies)?

Does anyone have a comprehensive resource listing results like the closures of common function spaces with certain topologies? Thanks.

It’s well-known that the continuous functions are dense in all functions on a space $$X$$, provided that $$X$$ has enough real continuous functions, e.g when $$X$$ is Tychonoff or even just functionally Hausdorff. So the fact I said sequential limits is quite important.