In this paper, we characterize local $T_{0}$ and $T_{1}$ quantale-valued gauge spaces, show how these concepts are related to each other and apply them to $mathcal{L}$-approach distance spaces and $mathcal{L}$-approach system spaces. Furthermore, we give the characterization of a closed point and $D$-connectedness in quantale-valued gauge spaces. Finally, we compare all these concepts to each o...

Let a denote an ideal of a local ring (R, m). Let M be a finitely generated Rmodule. There is a systematic study of the formal cohomology modules lim ←− H m(M/a M), i ∈ Z. We analyze their R-module structure, the upper and lower vanishing and non-vanishing in terms of intrinsic data of M, and its functorial behavior. These cohomology modules occur in relation to the formal completion of the pun...

Let T be the attractor of injective contractions f1, . . . , fm on R 2 that satisfy the Open Set Condition. If T is connected, ∂T is arcwise connected. In particular, the boundary of the Lévy dragon is arcwise connected.

One of the fundamental observations of theory of retracts says that any absolute retract for the class of all compacta is a locally connected continuum. However, when more restricted classes of spaces are considered, as for example hereditarily unicoherent continua, tree-like continua, dendroids, or hereditarily indecomposable continua, this is not necessarily the case (see e.g., [6, Corollarie...

In this paper, the concept of somewhat-connected space will be introduced and characterized. Its connection with the other well-known concepts such as the classical connectedness, the $omega_theta$-connectedness, and the $omega$-connectedness will be determined. Moreover, the concept of textit{somewhat}-continuous function from an arbitrary topological space into the product space will be chara...

OBJECTIVE To investigate the cognitive and neural correlates of discourse impairment in corticobasal syndrome (CBS). BACKGROUND Difficulty communicating is a frequent clinical manifestation in patients with CBS. However, the mechanisms underlying this disabling problem are not well understood. METHODS Twenty patients with CBS and 8 healthy seniors narrated a picture story. Narratives were a...