Definition The closure of a set $A$ is the intersection of all closed sets containing $A$. How does this relate to open sets?

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what is an open set in topology Informational

• Fundamentals Can a set be both open and closed?
• Intervals What is an open interval?
• Related Concepts How are open sets used in Urysohn's Lemma?
• Local Properties What is a path component of a topological space?
• Definition What is a locally path-connected space?
• Metric Spaces What is a manifold?
• Properties Does the collection of all open balls form a basis for the topology of a metric space?
• Metric Spaces What is the standard topology on $\mathbb{R}^n$?
• Real Line
• Cocountable Topology