On non-Baire rare sets in category bases
In this paper, we deal with non-Baire rare sets in category bases which forms $\aleph_0$-independent family, where a rare set is a common generalization of both Luzin and Sierpinski set.
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arXiv subjects
Abhit Chandra Pramanik
Publications and source records attributed to Abhit Chandra Pramanik.
A Kuratowski theorem revisited
If $f : X\mapsto Y$ is a function having Baire property from a metric space $X$ into a separable metric space $Y$ , then $f$ is continuous except on a set of first category. Kuratowski asked whether the condition of separability could be removed. Several attempts were done in the past to solve this problem. In fact, the first impressive attempt was initiated by Kunugi. This paper is aimed towards solving the problem of Kuratowski in category bases which generalizes the result of Kunugi.
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A note on sets avoiding rational distances in category bases
Michalski gave a short and elegant proof of a theorem of A. Kumar which states that for each set A in R, there exists a subset B of A which is full in A and such that no distance between points in B is a rational number. He also proved a similar theorem for sets in the Euclidean plane. In this paper, we generalize these results in some special types of category bases.
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Generalization of two theorems of Steinhaus in category bases
Here we unify two results of Steinhaus and their corresponding category analogues by extending them in the settings of category bases. We further show that in any perfect translation base, every abundant Baire set contains a full subset for which our second theorem fails.
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A few remarks on non-Baire sets in category bases
In this paper, we first establish some equivalent formulations of non-Baire sets in category bases. We then introduce the notion of an uniform non-Baire family of sets and show that there is an uniform non-Baire family inducing a decomposition of the whole space. This phenomenon is then interpreted in the context of the famous Banah-Mazur game.
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On completely non-Baire union in category bases
In this paper, we intend to show that under not too restrictive conditions, results much stronger than the one obtained earlier by Hejduk could be established in category bases.
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On non-Baire sets in category bases
In this paper, we prove a result on non-Baire sets in category bases which when applied together with a result of Grzegorek yeilds a comparatively stronger version of a decomposition theorem due to Ulam.
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