I was talking to one of my friends today and he said that open ball Convexity. No other properties link the two.
Is this true? It's just that it would be very helpful if there was a stronger statement that could be used!
My point is that the way you defined convexity can only be determined (visually since that is how you are describing it) in . If I asked you a similar question for the Banach space where is some arbitrary metric (or even topological) space I doubt you could graph it and tell me whether or not it's "convex"