Adjunction space

Summary

An adjunction space is obtained by gluing a space $Y$ onto a space $X$. The gluing uses a continuous map $f$ from a subspace $A$ of $Y$ into $X$. Each point $a$ of $A$ is identified with its image $f(a)$, and the result carries the quotient topology. Attaching cells to build CW complexes and the mapping cylinder are special cases.