Comment : Point set topology quiz
Comment : This quiz is designed to test your knowledge of point set topology notions in metric spaces,
Comment : such as open and closed sets, compact and connected sets, interior and adherent points, etc.

Question 1: Let E be a subset of a metric space (X,d). What does it mean for x to be an adherent point of E?


For every epsilon > 0, there exists a y in E such that d(y,x) < epsilon.
For every epsilon > 0, there exists a y in E such that 0 < d(y,x) < epsilon.
There exists epsilon > 0 and y in E such that 0 < d(y,x) < epsilon.
For every epsilon > 0 and all y in E, we have d(y,x) < epsilon.
For every y in E, there exists epsilon > 0 such that d(y,x) < epsilon.
There exists epsilon > 0 such that 0 < d(y,x) < epsilon for all y in E.
There exists y in E such that d(y,x) < epsilon for all epsilon > 0.