A mat of fibers with shape memory effect is obtained using commercially available components and a simple electrospinning process. For obtaining this goal, a blend of diglycidyl ether of bisphenol A (DGEBA) and Polycaprolactone (PCL) is electrospun and the obtained mats are cured by UV radiation, avoiding the melting of the PCL component. The cationic photoinitiator based on iodonium salts, used for the first time in the electrospinning process, increases the solution conductivity and consequently the spinnability of the blend. The obtained mats show shape memory properties through several cycles, with shape fixity ratios that range from 95 to 99% and shape recovery ratios of between 88 and 100% respectively.