Assume that $X$   is a compact  Hausdorff  space and $A\subset X$  is  a  retract of $X$.

>Is there a topological  groupoid structure on the topological  pair $(X,A)$ where,  in the corresponding small category,  $X$ and $A$ plays the role of morphisms and objects, respectively. 


**Edit:** Is there  a  theory which investigate such type of problems for  $A$ not necessarily a single point