What does component mean in classification of 1 manifolds?

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In classifying 1 manifolds one has the following lemma




Let $f:I rightarrow M $ and $g: J rightarrow M$ be parametrizations by arc-length. Then $f(I) cap g(J) $ has at most two components.




What does components mean here?

Also, I am reading Milnor's Topology from the differentiable viewpoint. He uses many concepts without defining and the reader is expected to know them already. Which is a good reference wherein I can find most of them?




general-topology reference-request




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  • 2




    Most likely (path) connected components?
    – freakish
    Jul 15 at 18:28










  • You can find these things in an ordinary topology book. I like Munkres "Topology".
    – Lee Mosher
    Jul 15 at 18:50














up vote
0
down vote

favorite












In classifying 1 manifolds one has the following lemma




Let $f:I rightarrow M $ and $g: J rightarrow M$ be parametrizations by arc-length. Then $f(I) cap g(J) $ has at most two components.




What does components mean here?

Also, I am reading Milnor's Topology from the differentiable viewpoint. He uses many concepts without defining and the reader is expected to know them already. Which is a good reference wherein I can find most of them?




general-topology reference-request




share|cite|improve this question















  • 2




    Most likely (path) connected components?
    – freakish
    Jul 15 at 18:28










  • You can find these things in an ordinary topology book. I like Munkres "Topology".
    – Lee Mosher
    Jul 15 at 18:50












up vote
0
down vote

favorite









up vote
0
down vote

favorite











In classifying 1 manifolds one has the following lemma




Let $f:I rightarrow M $ and $g: J rightarrow M$ be parametrizations by arc-length. Then $f(I) cap g(J) $ has at most two components.




What does components mean here?

Also, I am reading Milnor's Topology from the differentiable viewpoint. He uses many concepts without defining and the reader is expected to know them already. Which is a good reference wherein I can find most of them?




general-topology reference-request




share|cite|improve this question











In classifying 1 manifolds one has the following lemma




Let $f:I rightarrow M $ and $g: J rightarrow M$ be parametrizations by arc-length. Then $f(I) cap g(J) $ has at most two components.




What does components mean here?

Also, I am reading Milnor's Topology from the differentiable viewpoint. He uses many concepts without defining and the reader is expected to know them already. Which is a good reference wherein I can find most of them?





general-topology reference-request





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 15 at 18:22









mathemather

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  • 2




    Most likely (path) connected components?
    – freakish
    Jul 15 at 18:28










  • You can find these things in an ordinary topology book. I like Munkres "Topology".
    – Lee Mosher
    Jul 15 at 18:50












  • 2




    Most likely (path) connected components?
    – freakish
    Jul 15 at 18:28










  • You can find these things in an ordinary topology book. I like Munkres "Topology".
    – Lee Mosher
    Jul 15 at 18:50







2




2




Most likely (path) connected components?
– freakish
Jul 15 at 18:28




Most likely (path) connected components?
– freakish
Jul 15 at 18:28












You can find these things in an ordinary topology book. I like Munkres "Topology".
– Lee Mosher
Jul 15 at 18:50




You can find these things in an ordinary topology book. I like Munkres "Topology".
– Lee Mosher
Jul 15 at 18:50















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