Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets
The main aim of this paper is to prove that every non-σ-lower porous Suslin set in a topologically complete metric space contains a closed non-σ-lower porous subset. In fact, we prove a general result of this type on “abstract porosities.” This general theorem is also applied to ball small sets in...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/AAA.2005.221 |
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| _version_ | 1832562992151003136 |
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| author | Luděk Zajíček Miroslav Zelený |
| author_facet | Luděk Zajíček Miroslav Zelený |
| author_sort | Luděk Zajíček |
| collection | DOAJ |
| description | The main aim of this paper is to prove that every
non-σ-lower porous Suslin set in a topologically complete
metric space contains a closed non-σ-lower porous subset.
In fact, we prove a general result of this type on “abstract
porosities.” This general theorem is also applied to ball small
sets in Hilbert spaces and to σ-cone-supported sets in separable Banach spaces. |
| format | Article |
| id | doaj-art-03a69c9a75b14984810e564402f71b69 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-03a69c9a75b14984810e564402f71b692025-02-03T01:21:07ZengWileyAbstract and Applied Analysis1085-33751687-04092005-01-012005322122710.1155/AAA.2005.221Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous setsLuděk Zajíček0Miroslav Zelený1Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 186 75, Czech RepublicFaculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 186 75, Czech RepublicThe main aim of this paper is to prove that every non-σ-lower porous Suslin set in a topologically complete metric space contains a closed non-σ-lower porous subset. In fact, we prove a general result of this type on “abstract porosities.” This general theorem is also applied to ball small sets in Hilbert spaces and to σ-cone-supported sets in separable Banach spaces.http://dx.doi.org/10.1155/AAA.2005.221 |
| spellingShingle | Luděk Zajíček Miroslav Zelený Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets Abstract and Applied Analysis |
| title | Inscribing closed non-σ-lower porous sets into Suslin
non-σ-lower porous sets |
| title_full | Inscribing closed non-σ-lower porous sets into Suslin
non-σ-lower porous sets |
| title_fullStr | Inscribing closed non-σ-lower porous sets into Suslin
non-σ-lower porous sets |
| title_full_unstemmed | Inscribing closed non-σ-lower porous sets into Suslin
non-σ-lower porous sets |
| title_short | Inscribing closed non-σ-lower porous sets into Suslin
non-σ-lower porous sets |
| title_sort | inscribing closed non σ lower porous sets into suslin non σ lower porous sets |
| url | http://dx.doi.org/10.1155/AAA.2005.221 |
| work_keys_str_mv | AT ludekzajicek inscribingclosednonslowerporoussetsintosuslinnonslowerporoussets AT miroslavzeleny inscribingclosednonslowerporoussetsintosuslinnonslowerporoussets |