The closed neighborhood and filter conditions in solid sequence spaces
Let E be a topological vector space of scalar sequences, with topology τ; (E,τ) satisfies the closed neighborhood condition iff there is a basis of neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect to the topology π of coordinate-wise convergence on E; (E,τ) satisf...
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| Format: | Article |
| Language: | English |
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Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000773 |
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| _version_ | 1841524707465101312 |
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| author | P. D. Johnson, Jr. |
| author_facet | P. D. Johnson, Jr. |
| author_sort | P. D. Johnson, Jr. |
| collection | DOAJ |
| description | Let E be a topological vector space of scalar sequences, with topology τ;
(E,τ) satisfies the closed neighborhood condition iff there is a basis of
neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect
to the topology π of coordinate-wise convergence on E; (E,τ) satisfies the filter
condition iff every filter, Cauchy with respect to τ, convergent with respect
to π, converges with respect to τ. |
| format | Article |
| id | doaj-art-0d39c25b78214b699b2d60ae471faf60 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0d39c25b78214b699b2d60ae471faf602025-02-03T05:47:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112462563210.1155/S0161171289000773The closed neighborhood and filter conditions in solid sequence spacesP. D. Johnson, Jr.0Department of Algebra, Combinatorics, and Analysis, 120 Math Annex, Auburn University, Auburn 36849, Alabama, USALet E be a topological vector space of scalar sequences, with topology τ; (E,τ) satisfies the closed neighborhood condition iff there is a basis of neighborhoods at the origin, for τ, consisting of sets whlch are closed with respect to the topology π of coordinate-wise convergence on E; (E,τ) satisfies the filter condition iff every filter, Cauchy with respect to τ, convergent with respect to π, converges with respect to τ.http://dx.doi.org/10.1155/S0161171289000773 |
| spellingShingle | P. D. Johnson, Jr. The closed neighborhood and filter conditions in solid sequence spaces International Journal of Mathematics and Mathematical Sciences |
| title | The closed neighborhood and filter conditions in solid sequence spaces |
| title_full | The closed neighborhood and filter conditions in solid sequence spaces |
| title_fullStr | The closed neighborhood and filter conditions in solid sequence spaces |
| title_full_unstemmed | The closed neighborhood and filter conditions in solid sequence spaces |
| title_short | The closed neighborhood and filter conditions in solid sequence spaces |
| title_sort | closed neighborhood and filter conditions in solid sequence spaces |
| url | http://dx.doi.org/10.1155/S0161171289000773 |
| work_keys_str_mv | AT pdjohnsonjr theclosedneighborhoodandfilterconditionsinsolidsequencespaces AT pdjohnsonjr closedneighborhoodandfilterconditionsinsolidsequencespaces |