Baire theorem for ideals of sets

详细信息    查看全文

• 作者：A. Avilé ; s^a ; ^{avileslo@um.es" class="auth_mail" title="E-mail the corresponding author} ; V. Kadets^b ; ^{v.kateds@karazin.ua" class="auth_mail" title="E-mail the corresponding author} ; A. Pé ; rez^a ; ^{antonio.perez7@um.es" class="auth_mail" title="E-mail the corresponding author} ; S. Solecki^c ; ^{ssolecki@math.uiuc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Baire theorem ; Ideal of sets ; Nowhere dense ; Analytic set
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：445
• 期：2
• 页码：1221-1231
• 全文大小：379 K

文摘

We study ideals mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=64cf6f8988127ebc00de3b0bde3e3830" title="Click to view the MathML source">ImathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi mathvariant="script">Imi>math> on mmlsi2" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=2a07a14b254e0eb644aea6a1acbefe10" title="Click to view the MathML source">NmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll"><mi mathvariant="double-struck">Nmi>math> satisfying the following Baire-type property: m>if X is a complete metric space and  m>mmlsi3" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si3.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=9fa2099f970228f980dddb4169ec4b0e" title="Click to view the MathML source">{X_A:A∈I}mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><mo stretchy="false">{mo><msub><mrow><mi>Xmi>mrow><mrow><mi>Ami>mrow>msub><mo>:mo><mi>Ami><mo>∈mo><mi mathvariant="script">Imi><mo stretchy="false">}mo>math>m>is a family of nowhere dense subsets of X with  m>mmlsi4" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si4.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=312139aa46fb471b7eab9d34cda78816" title="Click to view the MathML source">X_A⊂X_BmathContainer hidden">mathCode"><math altimg="si4.gif" overflow="scroll"><msub><mrow><mi>Xmi>mrow><mrow><mi>Ami>mrow>msub><mo>⊂mo><msub><mrow><mi>Xmi>mrow><mrow><mi>Bmi>mrow>msub>math>m>whenever  m>mmlsi5" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si5.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=bfe7e1440d2005bd11cbc6037ae998e3" title="Click to view the MathML source">A⊂BmathContainer hidden">mathCode"><math altimg="si5.gif" overflow="scroll"><mi>Ami><mo>⊂mo><mi>Bmi>math>m>, then  m>mmlsi6" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1600216X&_mathId=si6.gif&_user=111111111&_pii=S0022247X1600216X&_rdoc=1&_issn=0022247X&md5=ed091ffe1b47681abc93273ea8a6f693" title="Click to view the MathML source">⋃_A∈IX_A≠XmathContainer hidden">mathCode"><math altimg="si6.gif" overflow="scroll"><msub><mrow><mo>⋃mo>mrow><mrow><mi>Ami><mo>∈mo><mi mathvariant="script">Imi>mrow>msub><msub><mrow><mi>Xmi>mrow><mrow><mi>Ami>mrow>msub><mo>≠mo><mi>Xmi>math>. We give several characterizations and determine the ideals having this property among certain classes like analytic ideals and P-ideals. We also discuss similar covering properties when considering families of compact and meager subsets of m>Xm>.