Basis for topology (intro)

This is a short lecture to introduce the concept of a basis for a topology on a set. In a nutshell, a basis for a topology are a collection of "a few" open sets that we can use to recover every open set in the topology. This is for my online topology class.

[yakovsushenok]

Thank you for these videos. Your explanations are very simple and your voice is very nice to listen to. You have one of the most calming voices))

[theo]

At 3:54, should the basis B for topology T not contain the empty set too? I don't see how you can create the empty set with just Unions of {1} and {2, 3}.

[ritchan]

For your example at 3:00 wouldn't you require the empty set to also be in the basis? By the definition, since the empty set is in the topology, there must be some subcollection of elements of B such that the union of that subcollection is the empty set ? But the empty set wasn't in your definition of B, so any union of elements of B is non empty and therefore we cannot get the empty set. Just wondering, thanks.

[vanessamichaels]

the B you write at 2:15 is too ambiguous. I can't tell if it's fancy B or regular B. :{

[awazin]

Very good playlist on topology :) I have a question which torments me concerning a base in topology. If in my basis B, I have only "wide" open sets like e.g. (a, a+2),(a+2,a+4) with a ∈ ℝ. Is this a basis? If for example I want to construct the open interval ( 1.5, 2.5), if I take the union of (0, 2) and (2, 4), 1.5 and 2.5 are well in this union? I think not but I would like to be sure :)