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.
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.

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
- 279 views
- $12.00
Related Questions
- How to properly write rational exponents when expressed as roots?
- Let $(X, ||\cdot||)$ be a normed space. Let $\{x_n\}$ and $\{y_n\}$ be two Cauchy sequences in X. Show that the seqience Show that the sequence $λ_n = ||x_n − y_n|| $ converges.
- Define $F : \mathbb{R}^ω → \mathbb{R}^ω$ by $F(x)_n = \sum^n_{k=1} x_k$. Determine whether $F$ restricts to give a well-defined map $F : (\ell_p, d_p) → (\ell_q, d_q)$
- Advanced Modeling Scenario
- Constructing Monotonic Sequences Converging to an Accumulation Point in a Subset of $\mathbb{R}$
- $\textbf{I would like a proof in detail of the following question.}$
- Prove the uniqueness of a sequence using a norm inequality.
- Related to Real Analysis