A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction $r:X̃\genfrac{}{}{0pt}{}{onto}{⟶}X$ such that all fibers $r^{-1}\left(x\right)$ are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum $Y_X$ is called a continuous pseudo-fan of a compactum X if there are a point $c\in Y_X$ and a family ℱ of pseudo-arcs such that $\bigcup ℱ=Y_X$, any subcontinuum of $Y_X$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic to X (with...