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Let $M (X, 𝒜)$ ( $M^{*} (X, 𝒜)$ ) be the $f$ -ring of all (bounded) real-measurable functions on a $T$ -measurable space $(X, 𝒜)$ , let $M_{K} (X, 𝒜)$ be the family of all $f \in M (X, 𝒜)$ such that $coz (f)$ is compact, and let $M_{\infty} (X, 𝒜)$ be all $f \in M (X, 𝒜)$ that ${x \in X : | f (x) | \geq \frac{1}{n}}$ is compact for any $n \in ℕ$ . We introduce realcompact subrings of $M (X, 𝒜)$ , we show that $M^{*} (X, 𝒜)$ is a realcompact subring of $M (X, 𝒜)$ , and also $M (X, 𝒜)$ is a realcompact if and only if $(X, 𝒜)$ is a compact measurable space. For every nonzero real Riesz map $ϕ : M (X, 𝒜) \to ℝ$ , we prove that there is an element $x_{0} \in X$ such that $ϕ (f) = f (x_{0})$ for every $f \in M (X, 𝒜)$ if $(X, 𝒜)$ is a compact measurable space. We confirm...

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

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Some more properties of $F_{ℐ}$ and regular $ℐ$ -closed sets in ideal topological spaces.

Some new deterministic and random variational inequalities and their applications.

Some observations on local uniform boundedness principles

Some observations on local uniform boundedness principles. II

Some problems and lines of investigation in general topology

Some problems on Suslin spaces and topological algebras

Some productive classes of maps which arc related to confluent maps

Some properly critical subsets of Euclidean spaces.

Some properties of algebras of real-valued measurable functions

Some properties of almost continuous multifunctions

Some properties of almost contra-precontinuous functions.

Some properties of $C_{p} (X)$

Some properties of cardinal functions, II

Some properties of g- and P-spaces

Some properties of irresolute multifunctions

Some properties of multiplication in the algebra $C (X)$ related to the dimension of $X$

Some properties of open and related mappings

Some properties of oscillation

Some properties of subsets, almost closed mappings and paracompactness.

Some properties of the functor $O_{β}$ .

Currently displaying 1981 – 2000 of 2509