index of properties of topological spaces

index of properties of topological spaces

Topological axioms

•

topological structures on sets

•

continuous maps

•

categories

,

functors

and

natural transformations

Compactness Properties

•

compact

•

countably compact

•

Lindelöf (

http://planetmath.org/

Lindelof

), finally compact (

http://planetmath.org/Lindelof

)

•

locally compact

•

metacompact

•

paracompact

•

strongly locally compact

•

sequentially compact

•

σ

-compact (

http://planetmath.org/SigmaCompact

)

•

σ

-locally compact

•

weakly countably compact

(

http://planetmath.org/LimitPointCompact

), limit point compact

Countability Properties

•

first countable

(

http://planetmath.org/FirstCountable

)

•

second countable

(

http://planetmath.org/SecondCountable

)

•

separable

Connectedness

Properties

•

biconnected

•

arc

connected

•

connected (

http://planetmath.org/ConnectedSpace

)

•

connected im kleinen

•

extremally disconnected

•

hyperconnected

•

locally arc connected

•

locally connected

•

locally path connected

•

path-connected

•

punctiform

•

scattered

•

totally disconnected

•

totally path disconnected

•

totally

separated

•

ultraconnected

Contractibility

Proprties

•

absolute retract

•

absolute neighborhood retract

•

contractible

to a point

•

locally simply connected

•

semi-locally simply connected

•

simply connected

•

locally homeomorphic

and covering spaces

•

fibrations

•

homotopy groups

•

homotopy

as a functor

•

homotopy type

•

lifting

properties of fibrations

Separation Properties

(

http://planetmath.org/SeparationAxioms

)

•

completely normal

•

completely regular

, Tychonoff

•

fully normal

•

fully

T

4

(

http://planetmath.org/FullyT4

)

•

normal

•

perfectly

T

4

•

perfectly normal

•

regular

•

semiregular

•

T

0

(

http://planetmath.org/T0Space

), Kolmogorov (

http://planetmath.org/T0Space

)

•

T

1

(

http://planetmath.org/T1Space

), Fréchet (

http://planetmath.org/T1Space

)

•

T

2

(

http://planetmath.org/T2Space

),

Hausdorff

(

http://planetmath.org/T2Space

)

•

T

2

⁤

1

2

(

http://planetmath.org/CompletelyHaussdorff

), completely Hausdorff

•

T

3

(

http://planetmath.org/SeparationAxioms

)

•

T

3

⁤

1

2

(

http://planetmath.org/SeparationAxioms

)

•

T

4

(

http://planetmath.org/SeparationAxioms

)

•

T

5

(

http://planetmath.org/SeparationAxioms

)

•

Urysohn, functionally Hausdorff

Subset Properties

•

open

•

closed

•

clopen

•

regular open

•

regular closed (

http://planetmath.org/RegularOpenSet

)

•

locally closed

•

dense

•

nowhere dense

•

meager

•

residual

•

separated sets (

http://planetmath.org/Separated

)

•

completely separated

sets (

http://planetmath.org/CompletelySeparated

)

Topological groups

•

full subgroup

Homology

Title

index of properties of topological spaces

Canonical name

IndexOfPropertiesOfTopologicalSpaces

Date of creation

2013-03-22 14:39:29

Last modified on

2013-03-22 14:39:29

Owner

rspuzio (6075)

Last modified by

rspuzio (6075)

Numerical id

29

Author

rspuzio (6075)

Entry type

Topic

Classification

msc 54-00

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