Mixing
Name and properties of certain class of subsets of $Bbb R^n$
I am looking for name or definition of a class of subsets of $ mathbb{R}^n$ with following properties (in brackets I am describing an alternative set of properties, also interesting for me) :
Subset $A$ is in class if:
$A$ is connected
$A$ is closed (alternatively open)- for each element $y$ of the image of the perpendicular projection of $A$ onto $mathbb{R}^{(n-1)}$, the preimage of $y$ is exactly closed (alternatively open) interval (closed interval can degenerate into a point).
Is there any theory studying properties of such sets?
I am especially interested in constructing CW-complexes where each cell has such property.
geometry multivariable-calculus reference-request cw-complexes
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
add a comment |
I am looking for name or definition of a class of subsets of $ mathbb{R}^n$ with following properties (in brackets I am describing an alternative set of properties, also interesting for me) :
Subset $A$ is in class if:
$A$ is connected
$A$ is closed (alternatively open)- for each element $y$ of the image of the perpendicular projection of $A$ onto $mathbb{R}^{(n-1)}$, the preimage of $y$ is exactly closed (alternatively open) interval (closed interval can degenerate into a point).
Is there any theory studying properties of such sets?
I am especially interested in constructing CW-complexes where each cell has such property.
geometry multivariable-calculus reference-request cw-complexes
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
add a comment |
I am looking for name or definition of a class of subsets of $ mathbb{R}^n$ with following properties (in brackets I am describing an alternative set of properties, also interesting for me) :
Subset $A$ is in class if:
$A$ is connected
$A$ is closed (alternatively open)- for each element $y$ of the image of the perpendicular projection of $A$ onto $mathbb{R}^{(n-1)}$, the preimage of $y$ is exactly closed (alternatively open) interval (closed interval can degenerate into a point).
Is there any theory studying properties of such sets?
I am especially interested in constructing CW-complexes where each cell has such property.
geometry multivariable-calculus reference-request cw-complexes
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
I am looking for name or definition of a class of subsets of $ mathbb{R}^n$ with following properties (in brackets I am describing an alternative set of properties, also interesting for me) :
Subset $A$ is in class if:
$A$ is connected
$A$ is closed (alternatively open)- for each element $y$ of the image of the perpendicular projection of $A$ onto $mathbb{R}^{(n-1)}$, the preimage of $y$ is exactly closed (alternatively open) interval (closed interval can degenerate into a point).
Is there any theory studying properties of such sets?
I am especially interested in constructing CW-complexes where each cell has such property.
geometry multivariable-calculus reference-request cw-complexes
geometry multivariable-calculus reference-request cw-complexes
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
edited Nov 21 '18 at 0:12
Tianlalu
3,09621038
3,09621038
asked Nov 20 '18 at 22:59
MJG
12
asked Nov 20 '18 at 22:59
MJG
12
asked Nov 20 '18 at 22:59
MJG
12
12
add a comment |
add a comment |
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