query: NECESSARY AND SUFFICIENT CONDITION for $x$ and $y$ lying in the same component of $R^{\omega}$ in uniform topology.
positive_passages.docid: 151051
positive_passages.text: connectedness of uniform topology
negative_passages.docid: 42913
negative_passages.text: Equivalence of the definition of the Subbasis of a Topology
negative_passages.docid: 85818
negative_passages.text: $E(|X-Y|)$ for $X$, $Y$ i.i.d and uniform on $[0,1]$
negative_passages.docid: 116768
negative_passages.text: Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
negative_passages.docid: 150796
negative_passages.text: Subspace topology and order topology (2)
negative_passages.docid: 149822
negative_passages.text: If $\omega \in \Omega^q(M)$, and $(\omega|_{U})_p = 0$, is $\omega_p = 0$?
negative_passages.docid: 135092
negative_passages.text: How exactly can't $\delta$ depend on $x$ in the definition of uniform continuity?
negative_passages.docid: 35547
negative_passages.text: Does $\{f_ng_n\}\to fg$ uniformly?
negative_passages.docid: 155794
negative_passages.text: Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
negative_passages.docid: 18334
negative_passages.text: Equivalence between CH and existence of certain sets in $\mathbb{R}^2$
negative_passages.docid: 138815
negative_passages.text: For which conditions on countable sets does continuity implies uniform continuity
negative_passages.docid: 99350
negative_passages.text: Are two norms equivalent if they induce the same topology on a vector space?
negative_passages.docid: 118049
negative_passages.text: Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
negative_passages.docid: 55749
negative_passages.text: Compactly supported continuous function is uniformly continuous
negative_passages.docid: 132946
negative_passages.text: Continuous and bounded imply uniform continuity?
negative_passages.docid: 108864
negative_passages.text: Showing that two topologies give rise to the same topology
negative_passages.docid: 52750
negative_passages.text: Prove that $f^\ast\omega=\det f \cdot \omega$