Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?

  • Thread starter cragar
  • Start date
  • Tags
    Interior
In summary, the statement Cl(X-A)=X-Int(A) is always true for topological spaces X and A, regardless of their dimensions. However, it should be noted that the concept of "dimension" may not be well-defined in all topological spaces. Additionally, it is important to clarify that X is a topological space and A is a subset of X, rather than both being topological spaces. Nonetheless, the statement can be easily verified and holds true in any topological space.
  • #1
cragar
2,552
3
If I have the statement Cl(X-A)=X-Int(A)
X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.
 
Physics news on Phys.org
  • #2
cragar said:
If I have the statement Cl(X-A)=X-Int(A)
X and A are topological spaces. Does this statement work in infinite dimensions and uncountable dimensions. I think it would just wondering.

What do you mean with "dimension" in topology in the first place?

But yes, the statement is always true as you can easily check for yourself.
 
  • #3
Most topological spaces do define "dimension". Nor does it make sense to talk about X and A both being topologica spaces. I think you mean X is a topological space and A is a subset of X. But it is true that in any topological space that the closure of X- A is X- the interior of A.
 

Related to Does Cl(X-A)=X-Int(A) work in infinite and uncountable dimensions?

1. What materials are best for interior walls?

The best materials for interior walls vary depending on factors such as budget, durability, and aesthetic preferences. Some common options include drywall, plaster, wood paneling, and brick.

2. How do I choose the right paint color for my interior?

Choosing the right paint color for your interior can be overwhelming. It's important to consider the natural lighting in the room, your existing furniture and decor, and the mood you want to create. It can also be helpful to get color swatches and test them out on your walls before committing to a color.

3. Can I use wallpaper in my interior?

Yes, wallpaper can be a great option for adding texture and design to your interior walls. However, it's important to properly prepare the walls before applying wallpaper and to choose a high-quality adhesive to ensure it stays in place.

4. How can I make a small interior space feel larger?

There are a few ways to make a small interior space feel larger. One is to use a light color palette, as dark colors can make a space feel more closed in. Another is to incorporate mirrors, which can create the illusion of more space. Additionally, using multi-functional furniture and decluttering can also help maximize space.

5. What are some eco-friendly options for interior design?

There are many eco-friendly options for interior design, such as using sustainable materials like bamboo or reclaimed wood, choosing energy-efficient appliances and lighting, and incorporating plants for natural air purification. It's also important to consider the environmental impact of any furniture or decor purchases and opt for second-hand or ethically-made items when possible.

Similar threads

Replies
6
Views
1K
Replies
35
Views
2K
Replies
3
Views
2K
Replies
8
Views
2K
  • Topology and Analysis
Replies
5
Views
252
Replies
4
Views
2K
Replies
2
Views
1K
  • Topology and Analysis
Replies
2
Views
1K
  • Topology and Analysis
Replies
2
Views
2K
  • Topology and Analysis
Replies
5
Views
2K
Back
Top