CONTENTSIntroduction............................................................................................................ 5I. Basic properties of Baire spaces................................................................... 61. Nowhere dense sets............................................................................................... 62. First and second category sets............................................................................. 83. Baire spaces............................................................................................................. 114. Isolated points and Baire spaces......................................................................... 15II. Concepts related to Baire spaces................................................................ 181. Baire spaces in the strong sense................................................................ 182. Baire category theorem........................................................................................... 193. Complete type properties which imply Baire...................................................... 194. Minimal spaces........................................................................................................ 24III. Characterizations of Baire spaces............................................................... 291. Blumberg type theorems........................................................................................ 292. Covering and filter characterizations.................................................................... 363. Characterizations of Baire spaces involving pseudo-complete spaces....... 374. The Banach-Mazur game........................................................................................ 385. Countably-Baire spaces......................................................................................... 41IV. The dynamics of Baire spaces..................................................................... 441. Images and inverse images of Baire spaces.................................................... 442. Baire space extensions.......................................................................................... 493. Hyperspaces and functions spaces..................................................................... 53V. Products of Baire spaces............................................................................... 561. Finite products.......................................................................................................... 562. Infinite products........................................................................................................ 603. k-Baire spaces.......................................................................................................... 644. Product counterexamples....................................................................................... 69Bibliography........................................................................................................... 72
@book{bwmeta1.element.zamlynska-209257a9-0350-4a43-aa72-b08059aee740,
author = {R. C. Haworth and R. A McCoy},
title = {Baire spaces},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1977},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-209257a9-0350-4a43-aa72-b08059aee740}
}
R. C. Haworth; R. A McCoy. Baire spaces. GDML_Books (1977), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-209257a9-0350-4a43-aa72-b08059aee740/