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There is no such thing as a two-dimensional space. By virtue of being a space, you are talking three dimensions. It sounds like what you're really asking is: What is a two-dimensional AREA bounded by an infinite set of points (or infinite number of sides - same thing)? Typically, that would be a circle...however you didn't specify the points all had to be equidistant from its center so it could be any irregular shape containing at least one curve (any curved portion would automatically have to contain infinite points). The best way to ask the question so that the only answer would be 'a circle' is: What is a two-dimensional area formed by an infinite set of points, all of which are equidistant from its center?

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Q: What is a two dimensional space formed by an infinite set of points?
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