6533b7ddfe1ef96bd1273fc7
RESEARCH PRODUCT
Precise bounds for the sequential order of products of some Fréchet topologies
Saliou SitouSzymon Doleckisubject
Discrete mathematicsClosure (topology)Topological spaceSequential spaceSquare (algebra)CombinatoricsProduct (mathematics)IdempotenceOrder (group theory)Countable setGeometry and TopologySequential orderFréchet (Fréchet-Urysohn) topologyProductMathematicsdescription
Abstract The sequential order of a topological space is the least ordinal for which the corresponding iteration of the sequential closure is idempotent. Lower estimates for the sequential order of the product of two regular Frechet topologies and upper estimates for the sequential order of the product of two subtransverse topologies are given in terms of their fascicularity and sagittality. It is shown that for every countable ordinal α, there exists a Lasnev topology such that the sequential order of its square is equal to α.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1998-04-01 | Topology and its Applications |