query: Can we say that Int(f(A)) a subset of f(Int(A))?
positive_passages.docid: 155063
positive_passages.text: Is Cl(f(A)) a subset of f(Cl(A))?
negative_passages.docid: 79281
negative_passages.text: Let $f : X \to Y$ be a function and $E \subseteq X$ and $F \subseteq X$. Show that in general
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 5230
negative_passages.text: Why can a 1 element set be a member of another set but not a subset of it?
negative_passages.docid: 158498
negative_passages.text: $A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
negative_passages.docid: 45485
negative_passages.text: Dimension of a subset
negative_passages.docid: 36093
negative_passages.text: Show rigorously that the sum of integrals of $f$ and of its inverse is $bf(b)-af(a)$
negative_passages.docid: 16056
negative_passages.text: Is empty set element of every set if it is subset of every set?
negative_passages.docid: 19452
negative_passages.text: Restriction of a Lebesgue integral to a subset of a measurable set.
negative_passages.docid: 49143
negative_passages.text: Showing $A \subset B \iff A\cap B=A$
negative_passages.docid: 19289
negative_passages.text: complement of a set and its measure
negative_passages.docid: 99458
negative_passages.text: Suppose $\int_{[a,b]}f=0,\text{ then }f(x)=0 \forall x\in[a,b]$
negative_passages.docid: 63717
negative_passages.text: Is the closure of a set equal to the closure of the closure of that set?
negative_passages.docid: 1821
negative_passages.text: Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
negative_passages.docid: 142583
negative_passages.text: Subsets of the Cantor set
negative_passages.docid: 83311
negative_passages.text: Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
negative_passages.docid: 120960
negative_passages.text: $f,g$ such that $\int fg = \int f \int g$