This interactive page is intended to demonstrate the definition of an open set. The red square represents an open set $$A$$. The yellow disc is an open ball of a point $$x\in A$$, that is $$B(x,\epsilon)$$ for some value of $$\epsilon$$. For any point in the open set $$A$$ it is possible to choose $$\epsilon$$ so that $$B(x,\epsilon)\subset A$$. For any point on the boundary of $$A$$ it is not possible to choose $$\epsilon$$ so that $$B(x,\epsilon)\subset A$$. The size of $$\epsilon$$ can be changed using the slider or (in older browsers) the drop down list. If the point is inside $$A$$ then pressing the 'Next point' button moves the point $$x$$ nearer to the boundary of $$A$$. Otherwise it gives a new boundary point. The 'Zoom' button zooms in on $$x$$ and the 'Shift left' button moves things to the left should this become necessary. The 'Reset' button resets the size and position.