 ##  [Topological Space](/topological-space) 

  ##  [Topological Space](https://natural.quantumdictionary.io/topological-space-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

A set X together with a collection τ of subsets of X (called open sets) such that ∅ and X belong to τ, τ is closed under arbitrary unions and finite intersections; τ is called a topology and (X, τ) is a topological space.

 
 ##  [Topological Space](https://mathlogic.quantumdictionary.io/topological-space-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A set equipped with a topology: a specified collection of open subsets that contains the empty set and the whole set, is closed under arbitrary unions and finite intersections.

 
 ##  [Topological Space](https://puremath.quantumdictionary.io/topological-space-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

A set X equipped with a collection τ of subsets called open sets such that the empty set and X belong to τ, arbitrary unions of members of τ belong to τ, and finite intersections of members of τ belong to τ.