All Questions

Does any real function have a Lipschitzian restriction on $D$, where $D$ is an infinite subset of $\Bbb R$ with an accumulation point?

I have a concrete question about continuous functions on $X = [0,1]^\omega$ (with the product topology). The map $f:X\to [0, 1]$ given by $(x_i)\mapsto \prod x_i$ is well-defined and Borel but not ...

Let $X$ be a metric space. Suppose a real-valued function $f:X\rightarrow \mathbb{R}$ is upper semicontinuous class $2$ if for all $c \in \mathbb{R},$ its preimage $f^{-1}(-\infty,c)$ is $F_{\sigma}$. ...

Let $f:\mathbb{R}\to\mathbb{R}$ be a periodic function with period $T$ and continuous everywhere except perhaps on a countable set, and have an image that's an uncountable subset of $\mathbb{R}$. Let $...

I have reached a deadlock to find a example to show that a compact Hausdorff space does not need to have a no non-trivial convergent sequence.(except $\beta\omega$) can you give me a example of ...