Hi, I'm not sure how else to phrase this. Let's say I have a linear transformation from R3 to R2. Let's assume in both spaces, I am using the standard topology with the standard euclidean distance metric. Does this mean that open sets in R3 will be mapped to open sets in R2 under this transformation? What if the transformation is not one to one or onto? If this is the case, I am not asking anyone to prove this to me but rather if you have any ideas what theorems I might look at to prove this myself? I was thinking connectedness would come in to play. Am I right in that assumption? Thanks so much!