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Subbase: Examples, Results using subbases & Definition

In topology in mathematics, a subbase (or subbasis, prebase, prebasis) for the topology τ of a topological space (X, τ) is a subcollection B {\displaystyle B} of τ {\displaystyle \tau } that generates τ , {\displaystyle \tau ,} in the sense that τ {\displaystyle \tau } is the smallest topology containing B {\displaystyle B} as open sets. A slightly…

Language: English [EN]
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Subbase topic overview

The analysis highlights Examples, Results using subbases and Definition as prominent areas in the source structure around Subbase.

Related topics
36
Source areas
4
Connected nodes
40
Extracted relationships
18
Concept neighborhoods
21
Bridge connections
40

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Examples · 15 topics
Results using subbases · 9 topics
Definition · 8 topics
Overview · 4 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Examples

Results using subbases

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Subbase connects Entity context

The extracted context around Subbase shows recurring relationship patterns in the source. For example, Subbase → Clearly, For, However, In, Less, T1, There, This Another extracted example is Subbase → Explicitly, Let, The, This. Use these groups to spot repeated connection types before inspecting the individual relationships.

Subbase

Top relations

related to Alternative definition · 8
Subbase → Clearly, For, However, In, Less, T1, There, This
related to Definition · 4
Subbase → Explicitly, Let, The, This
related to Alexander subbase theorem · 3
Subbase → James Waddell Alexander II, The, The Alexander Subbase Theorem
related to Results using subbases · 2
Subbase → One, That
is a · 1
Subbase → weaker notion than that of a base for a topology

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle topology open tau mathcal definition cover containing sets set topological space also isbn oclc elements theorem intersection intersections basis

Subbase relationships Subject–Predicate–Object triples

TTTA extracted 18 structured relationships around Subbase. Examples in this analysis include Subbase → is a → weaker notion than that of a base for a topology and Subbase → related to Alexander subbase theorem → The Alexander Subbase Theorem. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Subbaseis aweaker notion than that of a base for a topology0.90text
Subbaserelated to Alexander subbase theoremThe Alexander Subbase Theorem0.60section
Subbaserelated to Alexander subbase theoremJames Waddell Alexander II0.60section
Subbaserelated to Alexander subbase theoremThe0.60section
Subbaserelated to Alternative definitionLess0.60section
Subbaserelated to Alternative definitionIn0.60section
Subbaserelated to Alternative definitionThis0.60section
Subbaserelated to Alternative definitionHowever0.60section
Subbaserelated to Alternative definitionThere0.60section
Subbaserelated to Alternative definitionFor0.60section
Subbaserelated to Alternative definitionClearly0.60section
Subbaserelated to Alternative definitionT10.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Subbase bring nearby vocabulary together. In this analysis, examples include Displaystyle, Open and Tau. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Subbase
    • Displaystyle
    • Open
    • Tau
    • Space
    • Topology
    • Topological
    • Intervals
    • Elements
    • Theorem
    • Mathcal
    • Containing
    • Set
  • subbase
    • Displaystyle
    • Open
    • Tau
    • Space
    • Topology
    • Topological
    • Intervals
    • Elements
    • Theorem
    • Mathcal
    • Containing
    • Set
  • topological space
    • Space
    • Topological
    • Tau
    • Containing
    • Elements
    • Smallest
    • Mathcal
    • Subcollection
    • Subbase
    • Displaystyle
    • Every
    • Subbases
  • basis
    • Intervals
    • Usual
    • Intersection
    • Set
    • Generated
    • Intersections
    • Open
    • Tau
    • Equivalent
    • Every
    • Given
    • Mathbb
  • open set
    • Sets
    • Subcollection
    • Topology
    • Subbase
    • Every
    • Subbasic
    • Tau
    • Also
    • Elements
    • Generated
    • Topological
    • Mathbb
  • alexander subbase theorem
    • Displaystyle
    • Open
    • Tau
    • Use
    • Space
    • Topology
    • Topological
    • Intervals
    • Mathcal
    • Elements
    • Theorem
    • Containing
  • definition
    • Equivalent
    • Use
    • Intersections
    • Given
    • Union
    • One
    • Sets
    • Tau
    • Intersection
    • Subbase
    • Basis
    • Displaystyle
  • intersections
    • Given
    • Union
    • Use
    • Sets
    • Every
    • Since
    • Smallest
    • Subbases
    • Subcollection
    • Usual
    • Elements
    • One

Connections between topic areas Semantic bridges

For Subbase, one of the stronger structural bridges in this analysis connects Subbase with Examples. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Subbase — Examples · splits 25 ⟂ 16
Subbase — Results using subbases · splits 31 ⟂ 10
Subbase — Definition · splits 32 ⟂ 9
Subbase — Overview · splits 36 ⟂ 5

Map overview Semantic statistics

Subbase

Nodes41
Edges40
Triples18
Avg. degree1.95
Density0.04878
Components1

Source & methodology

TTTA analyzes the structure around Subbase to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Examples, Results using subbases & Definition, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Subbase · EN edition · Analysis: TopicsToTalkAbout

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