Recent content by fallgesetz

Ok, good point. I should clarify that originally I was asking for some embedding of a compact space which turns out to be hausdorff.

The colimit is defined in terms of a functor from an indexing category to another category(a diagram). In the examples I've seen of the colimit, the functor is always faithful, so my question is, are there any nonfaithful functors from index categories that come up in real life?

What does it mean to quotient a category by an object of the category? In particular, the problem in front of me specifies the category I ( a full subcategory of Top which is compact, contains coproducts, and the one point space), an object X of I, and asks me to do stuff with I/X.

I am not looking for an example of a compact & hausdorff space. I am asking -- if I have a compact space, is there a process by which I can make it a hausdorff space while preserving compactness. In a sense, I am looking for something like one point compactification(but not that, more like...

Is there a way to make a compact space hausdorff while preserving compactness?