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okay so welcome back to the playlist on functional analysis so were still continuing our study of metric spaces and now were going to see some more examples of metric spaces so weve done the L infinity space weve seen an example of a sequence based and now what were going to do is were going to look at functional spaces so were going to look at a function space where the set which were defining the metric structure on is going to be a set containing functions rather than sequences or more you could view sequences I suppose as functions from the natural numbers to the real numbers but in this case were going to look at were going to look at a set which is all continuous functions on a closed in for a B so were going to denote the set C a B is going to be used to denote the set containing all that say F which Maps a B onto the real ly of dear whats that in there onto the real line such that F is continuous now we have a lot of very nice theorems from real analysis about cont
