Geodesic
On sets with Baire property in topological spaces
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 59-65 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Steinhaus [9] prove that if a set $A$ has a positive Lebesgue measure in the line then its distance set contains an interval. He obtained even stronger forms of this result in [9], which are concerned with mutual distances between points in an infinite sequence of sets. Similar theorems in the case we replace distance by mutual ratio were established by Bose-Majumdar [1]. In the present paper, we endeavour to obtain some results related to sets with Baire property in locally compact topological spaces, particular cases of which yield the Baire category analogues of the above results of Steinhaus [9] and their corresponding form for ratios by Bose-Majumdar [1].
Steinhaus [9] prove that if a set $A$ has a positive Lebesgue measure in the line then its distance set contains an interval. He obtained even stronger forms of this result in [9], which are concerned with mutual distances between points in an infinite sequence of sets. Similar theorems in the case we replace distance by mutual ratio were established by Bose-Majumdar [1]. In the present paper, we endeavour to obtain some results related to sets with Baire property in locally compact topological spaces, particular cases of which yield the Baire category analogues of the above results of Steinhaus [9] and their corresponding form for ratios by Bose-Majumdar [1].
Classification : 28A05
Keywords: Baire property; first category; second category 
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Basu, S. On sets with Baire property in topological spaces. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/CMJ_2000_50_1_a7/

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