- #1

facenian

- 436

- 25

"Let ##f:A\rightarrow\prod X_\alpha## be defined by the equation

##f(a)=(f_\alpha(a))_{\alpha\in J}##;

Let ##Z## denote the subspace ##f(A)## of the product space ##\prod X_\alpha##. Show that the image under ##f## of each element of ##\mathcal{F}## is an open set of ##Z##."

The topology ##\mathcal{F}## of ##A## is given by the subbasis

$$\delta=\bigcup_{\alpha\in J}\{f_\alpha^{-1}(U):U\in\mathcal{F}_\alpha\}$$

Does anybody has an opinion?