# Subbasis for a topological space

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## Contents |

This article is about a basic definition in topology.VIEW: Definitions built on this | Facts about this | Survey articles about this

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## Definition

A **subbasis for a topological space** is a collection of open subsets of the topological space such that the following equivalent conditions hold:

- The set of subsets obtained by taking finite (possibly empty) intersections of these, form a basis for the topological space
- Every open subset is a countable union of finite intersections of these
- The topology on the space is the coarsest topology for which the given subsets are all open

No constraints are there for a collection of subsets to form a subbasis.