Compact Space is Pseudocompact
Jump to navigation
Jump to search
This article needs proofreading. Please check it for mathematical errors. If you believe there are none, please remove {{Proofread}} from the code.To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Proofread}} from the code. |
Theorem
Let $\struct {K, \tau}$ be a compact space.
Then:
- $\struct {K, \tau}$ is pseudocompact
Proof
Follows immediately from:
$\blacksquare$
Sources
1960: Leonard Gillman and Meyer Jerison: Rings of Continuous Functions: Chapter $1$: Functions on a Topological Space, $\S 1.4$