Благоустройство университетского кампуса как фактор создания имиджа учебного заведения

The article discusses the landscape improvement of the university campus, as a way to create the image of an educational institution, using the example of NArFU named after M.V. Lomonosov. The author proposes an algorithm for the development of the concept of architectural and landscape improvement of the campus. The purpose is the unification of the scattered spaces of the university, but also the positioning of the university in relation to other educational institutions, the presentation of the historical and cultural heritage of the region through green spaces, small architectural forms and visual imagery.

Fan-Gottesman Compactification and Scattered Spaces

Compactification is the process or result of making a topological space into a compact space. An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. There are a lot of compactification methods but we study with Fan- Gottesman compactification. A topological space X is said to be scattered if every nonempty subset S of X contains at least one point which is isolated in S. Compact scattered spaces are important for analysis and topology. In this paper, we investigate the relation between the Fan-Gottesman compactification of T3 space and scattered spaces. We show under which conditions the Fan-Gottesman compactification X* is a scattered.

A direct proof of a theorem of Jech and Shelah on PCF algebras

By using an argument based on the structure of the locally compact scattered spaces, we prove in a direct way the following result shown by Jech and Shelah: there is a family {Bα : α < ω1} of subsets of ω1 such that the following conditions are satisfied: (a) max Bα - α, (b) if α ∈ Bβ then Bα ⊆ Bβ, (c) if δ ≤ α and δ is a limit ordinal then Bα ∩ δ is not in the ideal generated by the sets Bβ, β < α, and by the bounded subsets of δ, (d) there is a partition {An : n ∈ ω} of ω1 such that for every α and every n, Bα ∩An is finite.

Scattered Spaces, Compactifications and an Application to Image Classification Problem

In this paper, we characterize spaces such that their one-point compactification is a scattered space. We study spaces such that their Wallman compactification is scattered and we give necessary and sufficient conditions on the subspace A to get its closure scattered. An application of scattered spaces to image classification problem is also presented.

FRAGMENTABILITY BY THE DISCRETE METRIC

In a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are ${\it\sigma}$-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.