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.