query: Prove that $F$ is locally constant iff the associated étale space over $X$ is a covering.
positive_passages.docid: 146789
positive_passages.text: A locally constant sheaf on a locally connected space is a covering space; Proof?
negative_passages.docid: 134859
negative_passages.text: Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
negative_passages.docid: 124844
negative_passages.text: Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
negative_passages.docid: 105700
negative_passages.text: Proving $\,f$ is constant.
negative_passages.docid: 70304
negative_passages.text: Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
negative_passages.docid: 89264
negative_passages.text: Connectedness in the Quotient Space
negative_passages.docid: 45222
negative_passages.text: When $f(x) = g(y)$ for almost every $(x,y)$, must $f$ and $g$ be constant almost everywhere?
negative_passages.docid: 83665
negative_passages.text: Prove a assertion concerning Lebesgue space
negative_passages.docid: 143043
negative_passages.text: When is a local homeomorphism a covering map?
negative_passages.docid: 158647
negative_passages.text: If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
negative_passages.docid: 101778
negative_passages.text: Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
negative_passages.docid: 145919
negative_passages.text: If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 138105
negative_passages.text: Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
negative_passages.docid: 82001
negative_passages.text: How to prove the function is a constant
negative_passages.docid: 69367
negative_passages.text: covering map with finite fibres and preimage of a compact set
negative_passages.docid: 51156
negative_passages.text: Function is Continuous When Restricted to Closed Sets Which Cover the Space