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Topological Space

Topological Space

Jun 23, 20231 min read

mathematics

up:: 026 MOC Topology

A topological space is a double (, where is a set and is a Topology of .

Examples

The real line is a topological space, alongside the standard topology .

Any Metric Space can be seen as a topological space as per their Metric Topology.

References

Sutherland, Wilson A. Introduction to metric and topological spaces. Oxford University Press, 2009.
Notas para um Curso de Física-Matemática, João Carlos Alves Barata. Cap. 27

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Examples
References

Backlinks

026 MOC Topology
20260223 Anotações Categorias e Capital (Espaço Comum de Organizações)
All sets are contained inside their closure
All sets contain their interior
Boundary (Topology)
Closure (Topology)
Closure preserves subset ordering
Hausdorff Space
Homeomorphism
Interior (Topology)
Interior preserves subset ordering
Measurable Space
Metric Topology
Sierpiński Space
The boundary is a closed set
The boundary of the boundary is a subset of the boundary
The boundary of the boundary is the boundary iff the boundary's interior is empty
The boundary of the set is the boundary of its complement
The closure is the complement of the interior of the complement
The closure of a finite union is the union of the closures
The closure of an arbitrary intersection is contained in the intersection of the closures
The interior is the complement of the closure of the complement
The interior of a finite intersection is the intersection of the interiors
The interior of an arbitrary union contains the union of the interiors
The real line is a topological space
Topologically Continuous Function
Topology

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