Abstract It is proved that for an extremally disconnected S -paracompact- T 2 spaces the properties semi-Menger, Menger, strongly star star-Menger, almost star-Menger are equivalent. We show a weakly semi-continuous (strongly θ -semi-continuous) image of semi-Menger (almost semi-Menger) (semi-Menger), respectively. The characterizations and also provided.

We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the interior of the closure of the interior operator. We show that the system wKD45, a weakened version of KD45, is sound and complete w.r.t. the class of all topological spaces. Moreover, we point out a problem regarding updates on extremally disconnected spaces that appears in the setting...

The purpose of this paper is to present and investigate a new class topological spaces known as Sw*-regular spaces, by utilizing the concept Sw-regular sets some its properties. which introduced in 2009 L. S. Abddullah A. B. Khalaf [1], properly contained S*- regular space [2], [3], means that Sw*- stronger form regular. Several characterizations, properties relationships with other such as, Sw...

In this paper we investigate the extremal richness of the multiplier algebra M(A) and the corona algebra M(A)/A, for a simple C∗-algebra A with real rank zero and stable rank one. We show that the space of extremal quasitraces and the scale of A contain enough information to determine whether M(A)/A is extremally rich. In detail, if the scale is finite, then M(A)/A is extremally rich. In import...

For a Banach space X its subset Y⊆X is called overcomplete if |Y|=dens(X) and Z linearly dense in for every Z⊆Y with |Z|=|Y|. In the context of nonseparable spaces this notion was introduced recently by T. Russo J. Somaglia but sets have been considered separable since 1950ties. We prove some absolute consistency results concerning existence nonexistence classical spaces. example: c0(ω1), C([0,...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

We present a new topological semantics for doxastic logic, in which the belief modality is interpreted as the closure of the interior operator. We show that this semantics validates Stalnaker’s epistemicdoxastic axioms [23], and indeed it is the most general (extensional) semantics validating them. We prove, among other things, that in this semantics the doxastic logic KD45 is sound and complet...

This note continues the study initiated in 2006 by P.L. Papini, R. R. Phelps and the author on some classical notions from finite-dimensional convex geometry in spaces of continuous functions. Let H be the family of all closed, convex and bounded subsets of a Banach space endowed with the Hausdorff metric. A completion of A ∈ H is a diametrically maximal set D ∈ H satisfying A ⊂ D and diamA = d...