# Math Help - Definition of sigma-compact

1. ## Definition of sigma-compact

I got two definitions of $\sigma$-compact: one is from Munkres' "Topology" page 289, ex. 10, as the image below;

the other is from wikipedia, which says $\sigma$-compact means the space is the union of countably many compact subspaces.
I can deduce from Munkres' version to wikipedia's version, but I can not do the converse. Can the converse hold? If not, which one is the right definition? Thanks.

2. Originally Posted by zzzhhh
I got two definitions of $\sigma$-compact: one is from Munkres' "Topology" page 289, ex. 10, as the image below;

the other is from wikipedia, which says $\sigma$-compact means the space is the union of countably many compact subspaces.
I can deduce from Munkres' version to wikipedia's version, but I can not do the converse. Can the converse hold? If not, which one is the right definition? Thanks.
The Wikipedia definition is what I have always seen as the standard definition of σ-compact. The Munkres definition looks superficially stronger, and it's not clear to me whether the two definitions are equivalent.