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C.F.G
C.F.G
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A question on MobiusMöbius strip and Jordan curve

If $A\subset \Bbb R^2$ then is the following statement true?

$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq \text{Mobius strip}\quad\iff\quad A\,\,\, \text{is a Jordan curve}.$$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq$ Möbius strip $\iff A$ is a Jordan curve.

A question on Mobius strip and Jordan curve

If $A\subset \Bbb R^2$ then is the following statement true?

$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq \text{Mobius strip}\quad\iff\quad A\,\,\, \text{is a Jordan curve}.$

A question on Möbius strip and Jordan curve

If $A\subset \Bbb R^2$ then is the following statement true?

$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq$ Möbius strip $\iff A$ is a Jordan curve.

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Jeff Strom
Jeff Strom
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A question on MubiusMobius strip and Jordan curve

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C.F.G
C.F.G
  • 4.2k
  • 6
  • 31
  • 65

A question on Mubius strip and Jordan curve

If $A\subset \Bbb R^2$ then is the following statement true?

$\{(x,y)\in {(A\times A)/ \sim}\,\,\,|\,\, (x,y)\sim(y,x)\}\simeq \text{Mobius strip}\quad\iff\quad A\,\,\, \text{is a Jordan curve}.$