chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2026-27-1-134-138cheb-2188Research ArticleКраткие сообщенияНекоторые независимые результаты в идеальных пространствах РотбергераSome independent results on Ideal-Rothberger spacesПрасенджитБалPrasenjitBal

доктор математики

Ph.D. in Mathematics

balprasenjit177@gmail.comИнститут дипломированных финансовых аналитиков Индийского университета ТрипураИндияThe Institute of Chartered Financial Analysts of India University TripuraIndia202615042026271134138Copyright © Прасенджит Б., 20262026Прасенджит Б.Prasenjit B.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/2188

В этой статье мы покажем, что в обычном 𝑝-пространстве для каждой пары непересекающихся идеального множества Ротбергера и замкнутого множества существует пара непересекающихся открытых множеств, таких, что одно содержит замкнутое множество, а дополнение другого по отношению к идеальному множеству Ротбергера находится в соответствующем подидеале. Более того, мы демонстрируем, как семейства замкнутых множеств могут быть использованы для описания идеальных пространств Ротбергера.

In this article we show that in a regular 𝑝-space, for every pair of disjoint ideal Rothberger set and closed set there is a pair of disjoint open sets such that one contains the closed set and other one’s complement with respect to the ideal rothberger set is in the corresponding sub ideal. Moreover, we demonstrate how families of closed sets can be used to describe the ideal Rothberger spaces.

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The authors declare that there are no conflicts of interest present.