> **Possible Duplicate:**  
> [Largest Hausdorff quotient](https://mathoverflow.net/questions/78175/largest-hausdorff-quotient)  


Is there a left adjoint to ${\mathbf{Haus}}\to{\mathbf{Top}}$? Here ${\mathbf{Haus}}$ is the full subcategory of Hausdorff spaces in ${\mathbf{Top}}$? 

If this is too much to ask, how about a left adjoint to the restriction to compact spaces ${\mathbf{CptHaus}}\to{\mathbf{CptTop}}$?