After seeing all the other topology problems be left out to dry, I'm not exactly confident Ill get help, but ill try anyway.

So heres a photo of my problem, since im not the best at latex

ok i get that we have to start with let $\displaystyle \epsilon$ > 0 then we should have $\displaystyle \delta$ > 0 as well right? well after that im seriously sunk, cause I dont know what we would use as as I: (X, d*). I assume whatever we use as that is the one we set < $\displaystyle \delta$ then since its a function to (R,d) it must have |t-a|< $\displaystyle \epsilon$ but even if all that is right, i wouldnt know what to do there. Any help would be amazing