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include the mathematical definition from Adams and Franzosa
'''Quotient topology''' is a concept in the branch of [[mathematics]] known as [[topology]]. Where there is only one map ''f: X -> Y'', this is a [[strong topology]] on ''Y'' and it is defined as the quotient topology induced on ''Y'' by ''f''.
'''Quotient topology''' is a concept in the branch of [[mathematics]] known as [[topology]].
==Definition==
Let <math>X</math> be a topological space, and <math>A</math> a set, and let <math>p \colon X \to A</math> be a [[surjection]]. The quotient topology on <math>A</math> induced by <math>p</math> is the topology whose open sets are the sets <math>U \subseteq A</math> such that <math>p^{-1}(U)</math> is an open set in <math>X</math>.<ref>C. Adams and R. Franzosa. ''Introduction to Topology: Pure and Applied''. Upper Saddle River, NJ: Pearson Prentice Hall, 2008. p. 89</ref>
==References==
{{Reflist}}
[[category:topology]]
[[category:topology]]