Talk:Monomorphism

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let X → D denote the (continuous) restriction map from a topological space X to a dense subset D

This doesn't make sense to me. How is this "restriction map" defined? If X = R and D = Q, how is the image of sqrt(2) defined?? I think this might be reversed from the correct formulation: let i : D --> X be the injective inclusion of a dense subset of a space X. Then i is both monic and epic in Top, but only injective as a set function, not surjective (i.e. taking the forgetful functor, it's image is monic is Set, but not epic.)

No, the example can't be backwards. The inclusion map is injective. We are looking for a continuous map which is not injective but still is a monomorphism in the category of topological spaces. However, it is not clear to me that the example works. As you say, is there an example of a space which can be continuous mapped onto a dense subset? Clearly one cannot continuously map R onto Q since Q is disconnected. Do any examples exist? -- Fropuff 03:59, 2005 Apr 1 (UTC)

Sorry, just noticed the example was botched. I removed it and will look for an example elsewhere. - Gauge 08:22, 2 Apr 2005 (UTC)

Found an example. Cheers, Gauge 08:59, 2 Apr 2005 (UTC)

[edit] related concepts

I do not see the need for new pages on the notions of strong monomorphism, etc. I would suggest giving the precise definition here and creating redirects from those if necessary. Magidin 05:20, 6 February 2006 (UTC)