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How do I define an open set using only the four axioms of topological neighborhoods, as per the Wikipedia article on topological spaces? The intuitive definition of an open set is that it's a set of points on a real number line containing only points at which there is room for some hypothetical...

I am struggling to define an open set using the four axioms of a topological neighborhood, as per the Wikipedia article "Topological spaces." An open set on a real number line is a set of points that contains only interior points, meaning that there is always room for some hypothetical particle...