I was hoping you guys could help me in understanding some vector spaces of infinite dimension. My professor briefloy touched n them (class on linear algebra), but moved on rather quickly since they are not our primary focus. He gave me the example of the closed unit interval where f(x) is continuous over I. From my studies in analysis, I understand how there exists an infinite amount of points within the interval, and am having trouble on connecting this fact to the dimension of the space. Can anyone offer me a more complete explanation on this? I'd also love to hear some other infinite dimension spaces and their prospective applications. I don't like only grasping things of R^n ;). Thanks so much!