Alderaz, Shbani Fatma Hussien2026-05-182026-05-182019https://hdl.handle.net/10566/22502This dissertation is a presentation to generalize boundedness and pseudocompactness in pointfree topology. We first obtain and introduce a boundedness notion for elements of a frame. This is then further inspiration to introduce a definition of bounded frame homomorphism whose domain may be any frame E, not just the frame of open sets of the reals.enFrameBounded frame elementPseudocompact spacePseudocompact frameE-pseudocompact frameThesis