Latest update

- 'es mit etwas versuchen'
- Recognizing cases with multiple objects
- SP Online : The SPListItem being updated was not retrieved with all taxonomy fields
- SP Online : structure of folders
- Show custom content in Main Page Summary
- Separate home page per domain in multilingual setup (i18n)
- Changing homepage
- How to change the Front page for the Commerce Kickstart distribution?
- Make page.tpl.php and page--front.tpl.php share same html
- Redirect from root and not page itself
- What's inside “print render($page['content'])”? I want to style my front page in Omega subtheme
- Block Module jQuery Slider for Homepage
- Drupal front page and facebook crawlers
- Meta Tags on Frontpage
- Custom region in theme not on front page?
- Separate frontpage per domain?
- view and Content:user issue
- How to optimize this code to save time?
- Moore-Neighbor Tracing Algorithm
- print content of two binary search trees in sorted order

# Ideal chain in $\mathbb{R},\mathbb{Q}, \mathbb{N}$

2017-12-13 13:57:07

An ideal $I$ in $C(X)$ is called $z$-ideal if $Z(f) \in Z(I) $ implies $f \in I$.

$Z(f)=\{ x \in X : f(x) = 0 \} $

Help me solve the following problem?

1: Find a chain of $z$ -ideals in $C(\mathbb{R})$ ( under set

inclusion ) that is in one - one ,order-pereserving corresponding with

$\mathbb{R}$ itself.

2: Find a chain of $z$ -ideals in $C(\mathbb{Q})$ is one - one

,order-pereserving corresponding with $\mathbb{R}$.

Do the same for $C(\mathbb{N})$?