Interior of union of two sets with empty interior
Let $X$ and $Y$ be subsets of $\mathbb{R}^n$. If $\text{int}(X)$ and $\text{int}(Y)$ are empty sets and $X$ is closed, then $\text{int}(X \cup Y)$ is an empty set.
Mona Vinci
39
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Erdos
4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 865 views
- $12.00
Related Questions
- Measure Theory and the Hahn Decomposition Theorem
- [Real Analysis] Show that the set $A$ is uncountable. Use this result to show that ${\displaystyle\mathbb {R}}$ is uncountable.
- Uniform convergence of functions
- real analysis
- Banach fixed-point theorem and the map $Tf(x)=\int_0^x f(s)ds $ on $C[0,1]$
- Prove that $S \subseteq X$ is nowhere dense iff $X-\overline{S}$ is dense.
- Sigma-Algebra Generated by Unitary Subsets and Its Measurable Functions
- A function satifying $|f(x)-f(y)|\leq |x-y|^2$ must be constanct.
