Properties (60)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Topology
|
| gptkbp:hasDepartment |
A topology where every point has a countable local base.
|
| gptkbp:hasExhibition |
First_Countable_Hausdorff_Space.
First_Countable_Space. First_Countable_Space_in_Analysis. First_Countable_Space_in_Topology. Locally_Compact_Space. Locally_Euclidean_Space. Locally_First_Countable_Space. |
| gptkbp:hasSpecialty |
Every first countable space is sequential.
|
| https://www.w3.org/2000/01/rdf-schema#label |
First Countable Topology
|
| gptkbp:isAvenueFor |
Metric_Spaces
|
| gptkbp:isCharacterizedBy |
Countable neighborhoods.
Countable bases at each point. Countable bases for neighborhoods. Countable local bases at each point. Countable local bases. Countable neighborhoods around points. Countable bases for open sets. Countable convergence. Countable local bases for convergence. Countable neighborhoods for each point. Countable open covers. Countable open sets. Countable sequences of neighborhoods. Sequential compactness. |
| gptkbp:isEquippedWith |
Compact_Topology.
Non-First_Countable_Topology. |
| gptkbp:isFoundIn |
Functional Analysis.
Real Analysis. Point-Set_Topology. |
| gptkbp:isRelatedTo |
Countable Set
Continuity. Convergence. Topology of Convergence. Topology of Limits. Topology of Sequences. Closure Operator. Compactness. Local Base Topology of Closure. Topology of Neighborhoods. Baire_Category_Theorem. Hausdorff_Space. Sequential_Continuity. Topological_Spaces. Topology_of_Compactness. Topology_of_Convergence_Sequences. Topology_of_Limits_and_Convergence. |
| gptkbp:isSuitableFor |
Second_Countable_Topology
|
| gptkbp:isUsedIn |
Analysis
Set Theory. Topology of Metric Spaces. Topology of Open Sets. Topology of Continuous Functions. General_Topology. Topology_of_Compact_Spaces. Topology_of_Function_Spaces. Topology_of_Sequential_Spaces. |
| gptkbp:isUtilizedFor |
gptkb:First_Countable_Space
|