On sets with Baire property in topological spaces
Czechoslovak Mathematical Journal (2000)
- Volume: 50, Issue: 1, page 59-65
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topBasu, S.. "On sets with Baire property in topological spaces." Czechoslovak Mathematical Journal 50.1 (2000): 59-65. <http://eudml.org/doc/30541>.
@article{Basu2000,
abstract = {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].},
author = {Basu, S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Baire property; first category; second category; Baire property; first category; second category},
language = {eng},
number = {1},
pages = {59-65},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On sets with Baire property in topological spaces},
url = {http://eudml.org/doc/30541},
volume = {50},
year = {2000},
}
TY - JOUR
AU - Basu, S.
TI - On sets with Baire property in topological spaces
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 59
EP - 65
AB - 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].
LA - eng
KW - Baire property; first category; second category; Baire property; first category; second category
UR - http://eudml.org/doc/30541
ER -
References
top- On some properties of sets with positive measures, Annali dell Unversita di Ferrara X(1) (1962), 1–11. (1962)
- On the difference of two second category Baire sets in a topological group, Proc. Amer. Math. Soc. 47(1) (1975), 257–258. (1975) MR0349893
- On ratio sets of real numbers, Indian. Jour. Pure. Appl. Math. 23(1) (1993), 15–20. (1993) MR1203244
- 10.4064/fm-71-2-165-169, Fund. Math. 71(2) (1971), 163–169. (1971) Zbl0214.37403MR0293363DOI10.4064/fm-71-2-165-169
- 10.1007/BF02851150, Rend. Circ. Mat. Palermo (2)31 (1982), 404–414. (1982) MR0693586DOI10.1007/BF02851150
- Measure and Category, Springer-Verlag, 1980. (1980) Zbl0435.28011MR0584443
- Sur les ensembles de distance, Memoires Neuchatel Universite, 1938–39. (1938–39)
- A generalization of a theorem of S. Piccard, Proc. Amer. Math. Soc. 74(2) (1979), 281–282. (1979) Zbl0414.54010MR0516480
- 10.4064/fm-1-1-93-104, Fund. math. 1 (1920), 93–104. (1920) DOI10.4064/fm-1-1-93-104
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.