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EmptyRegion[n]

represents the empty subset of .

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Basic Examples  
Scope  
Regions  
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EmptyRegion

EmptyRegion[n]

represents the empty subset of .

Examples

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Basic Examples  (2)

Embedding dimension:

Wolfram Language code: RegionEmbeddingDimension[EmptyRegion[7]]

Region membership condition:

Wolfram Language code: RegionMember[EmptyRegion[3], {x, y, z}]

Scope  (8)

Regions  (8)

Embedding dimension:

Wolfram Language code: RegionEmbeddingDimension[EmptyRegion[3]]

Geometric dimension:

Wolfram Language code: RegionDimension[EmptyRegion[3]]

Point membership test:

Wolfram Language code: RegionMember[EmptyRegion[4], {1, 2, 3, 4}]

Get conditions for point membership:

Wolfram Language code: RegionMember[EmptyRegion[4], {x, y, z, t}]

Distance from a point:

Wolfram Language code: RegionDistance[EmptyRegion[2], {1, 1}]

Signed distance from a point:

Wolfram Language code: SignedRegionDistance[EmptyRegion[2], {1, 1}]

Nearest point in the region:

Wolfram Language code: RegionNearest[EmptyRegion[2], {1, 1}]

An empty region is bounded:

Wolfram Language code: BoundedRegionQ[EmptyRegion[3]]
Wolfram Language code: RegionBounds[EmptyRegion[3]]

Integrate over an empty region:

Wolfram Language code: Integrate[x ^ 2 + y ^ 2 + z ^ 2, {x, y, z}∈EmptyRegion[3]]

Optimize over it:

Wolfram Language code: ℛ = EmptyRegion[2];
Wolfram Language code: MinValue[{(x - 3)^2(y - 1)^2 + 1, {x, y}∈ℛ}, {x, y}]

Solve over an empty region:

Wolfram Language code: ℛ = EmptyRegion[2];
Wolfram Language code: Reduce[x^2 + y^2 == 1 && {x, y}∈ℛ, {x, y}]
Wolfram Research (2014), EmptyRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/EmptyRegion.html.

Text

Wolfram Research (2014), EmptyRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/EmptyRegion.html.

CMS

Wolfram Language. 2014. "EmptyRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EmptyRegion.html.

APA

Wolfram Language. (2014). EmptyRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EmptyRegion.html

BibTeX

@misc{reference.wolfram_2026_emptyregion, author="Wolfram Research", title="{EmptyRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/EmptyRegion.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_emptyregion, organization={Wolfram Research}, title={EmptyRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/EmptyRegion.html}, note=[Accessed: 13-June-2026]}