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I'm not sure how else to phrase this.

Let's say I have a linear transformation from R^{3}to R^{2}. 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 R^{3}will be mapped to open sets in R^{2}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!

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# Open sets preserved in linear transformation that isn't bijective?

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