The (Weak) Full Projection Property for Inverse Limits with Upper Semicontinuous Bonding Functions

Inverse Limits with Upper Semi-continuous Bonding Functions Whose Inverse Functions are Continuous

“…It is easy to see that f i is indecomposable, f −1 i is continuous, and A (f i ) is dense in G(f i ). Also, by [ Next, we deal with topics in [2]. In [2], Banič,Črepnjak, Merhar, and Milutinovič gave some results about the full projection property, the weak full projection property (see [2,Definition 5]), and the inverse limit property (see Definition 6.9).…”

“…Also, by [ Next, we deal with topics in [2]. In [2], Banič,Črepnjak, Merhar, and Milutinovič gave some results about the full projection property, the weak full projection property (see [2,Definition 5]), and the inverse limit property (see Definition 6.9). Also, in [2], they posed some problems with respect to the (weak) full projection property and the inverse limit property.…”

“…The full projection property and the continuum full projection property have been studied by many authors. For example, see [2,[6][7][8][12][13][14].…”

“…6, we give the examples of inverse sequences, such that each of their factor spaces is a simple closed curve and their inverse limits are indecomposable continua. Also, we give the negative answer to [2,Problem 10].…”

Mahavier completeness and classifying diagrams

“…Of course, inverse limits of spaces are nothing but categorical limits in the category Top of topological spaces and continuous mappings, and it is natural to ask whether the slogan generalises. Results addressing some categorical aspects of generalised inverse limits directly can be found in [4,26], but they were only partially successful in fully restoring the link with category theory, and the difficulty can be traced to the following phenomenon. Consider the functor T : Top → Top which maps a space X to T (X), the space of all subsets of X, endowed with the upper Vietoris topology.…”