# Create lower dimensional manifolds in a larger dimension

**URL:** https://discourse.julialang.org/t/create-lower-dimensional-manifolds-in-a-larger-dimension/89848
**Category:** New to Julia
**Tags:** math
**Created:** [November 6, 2022, 6:40pm UTC](https://discourse.julialang.org/t/create-lower-dimensional-manifolds-in-a-larger-dimension/89848 "2022-11-06T18:40:52Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![JosieG](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/josieg/32/36221_2.png) [@JosieG](https://discourse.julialang.org/u/JosieG)
#### Post date: [November 6, 2022, 6:40pm UTC](https://discourse.julialang.org/t/create-lower-dimensional-manifolds-in-a-larger-dimension/89848/1 "2022-11-06T18:40:52Z")

</div>

I’m very new to Topology. Suppose I want to create a 1-dim/2-dim/3-dim manifold, which is in a 20-dim space, and I will apply some dimension reduction, like PCA to their original dim. Is there anyway to do that? I went through the website and my current code is

```julia
struct ScaledSphere{N} <: AbstractDecoratorManifold{ManifoldsBase.ℝ} where {N}
    radius::Float64
end
ScaledSphere(radius, n) = ScaledSphere{n}(radius)
Base.show(io::IO, M::ScaledSphere{n}) where {n} = print(io, "ScaledSphere($(M.radius),$n)")
S = ScaledSphere(1.5, 2)

```

I know this is 2-dim sphere, but how to deal with 20 dimensions?