query: Is "total boundedness" a topological property?
positive_passages.docid: 17165
positive_passages.text: Is total boundedness a topological property?
negative_passages.docid: 125610
negative_passages.text: Space of bounded continuous functions is complete
negative_passages.docid: 150331
negative_passages.text: Whenever $f=T(x)$ then $f(x) \geq 0$. Prove $T$ is bounded by closed graph theorem.
negative_passages.docid: 66239
negative_passages.text: Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
negative_passages.docid: 120252
negative_passages.text: Equivalences of bounded sets definitions
negative_passages.docid: 88028
negative_passages.text: Topology - closures of intervals with the order topology
negative_passages.docid: 154682
negative_passages.text: G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
negative_passages.docid: 82745
negative_passages.text: Showing Entire Function is Bounded
negative_passages.docid: 118134
negative_passages.text: If $\psi h$ is in $L^2$ for all $h\in L^2$, must $\psi$ be essentially bounded?
negative_passages.docid: 72190
negative_passages.text: Topological proof on discrete topology where $X$ is infinite
negative_passages.docid: 68724
negative_passages.text: $||T-I|| < 1$ implies that $T$ is invertible.
negative_passages.docid: 120648
negative_passages.text: Proof Check: Every Cauchy Sequence is Bounded
negative_passages.docid: 38840
negative_passages.text: Tightness and Inner Regularity
negative_passages.docid: 105791
negative_passages.text: Does separability imply the Lindelöf property?
negative_passages.docid: 127900
negative_passages.text: Interior of closure of open set in topological space
negative_passages.docid: 132946
negative_passages.text: Continuous and bounded imply uniform continuity?
negative_passages.docid: 48174
negative_passages.text: Are countable topological spaces second-countable?