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Hatcher uses the words "path-component" and "component" without giving their definition. The first occurrence of "path-component" is on p. 19, exercise 12. The first occurrence of "component" is on p. 6, example 0.2.

I think "path-component" means "path-connected component". But what is a "component" of a topological space? He seems to use it to mean a $k$-cell, for any $k$. Is this the definition?

Thank you for your help.

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I think it just means "connected component" ( – joriki Mar 10 '11 at 10:13
up vote 2 down vote accepted

Hatcher just means connected components. It is assumed that if you are reading Hatcher you have some background in general topology.

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