Weak Strictly Persistence Homeomorphisms and Weak Inverse Shadowing Property and Genericity

Weak Inverse Shadowing and Genericity

We study the genericity of the first weak inverse shadowing property and the second weak inverse shadowing property in the space of homeomorphisms on a compact metric space, and show that every shift homeomorphism does not have the first weak inverse shadowing property but it has the second weak inverse shadowing property.

Constructions of Weak Inverse Property Loops

z-weak ideals and prime weak ideals

In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

Lowness for Weak Genericity and Randomness

We prove that lowness for weak genericity is equivalent to semicomputable traceability which is strictly between hyperimmune-freeness and computable traceability. We also show that semi-computable traceability implies lowness for weak randomness. These results refute a conjecture raised by several people.

The Weak Lefschetz Property, Inverse Systems and Fat Points

In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connected to t...