Retracts and retracts by pseudo-deformation of continua without R3-sets, R4-continua, and s-points

A continuum is a nondegenerate, compact, connected, metric space. A topological property P is invariant under retraction provided that each retract of a continuum having P has P, and P is reversible under retraction by pseudo-deformation if the condition a subcontinuum of a continuum X has P implies that X has P. In this paper, we prove that the absence of $R^3$-sets, the absence of $R^4$-continua and the absence of s-points are reversible under retractions by pseudo-deformation, and the absence of $R^3$-sets and the absence of $R^4$-continua are invariant under retractions while the absence of s-points is not.