Lets say I got to prove that $(X_1\times X_2 \times X_3\times \cdots X_{n-1})\times X_n$ is homeomorphic to $(X_1\times X_2 \times X_3\times \cdots X_n)$
I just define the function as
$f((x_1,x_2,\cdots x_{n-1}),x_n)=(x_1,x_2\cdots x_n)$ .... THen I can prove it right @anon
I have a question about this property:
Let $\lim\limits_{n\to\infty} a_n = a$, then $\lim\limits_{n\to\infty}(ca_n) = ca$ for all $c \in \mathbb R$
If we consider when $c$ doesnt equal $0$, my book's proof says:
Consider $|ca_n - ca| < \varepsilon$, then we have $|c||a_n-a|<\varepsilon$.
Si...
