query: Besides $ω_{(1)}$ what space has Stone-Cech compactification and one-point compactification the same?
positive_passages.docid: 145415
positive_passages.text: Examples of almost compact spaces.
negative_passages.docid: 47251
negative_passages.text: Non-compactness of $\mathbb{R}$ with the cocountable topology
negative_passages.docid: 102048
negative_passages.text: Closure of a compact set in Regular space $ X $
negative_passages.docid: 2871
negative_passages.text: Spaces with equal homotopy groups but different homology groups?
negative_passages.docid: 102485
negative_passages.text: Showing that a topological space is ${\rm T}_1$
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability
negative_passages.docid: 59194
negative_passages.text: Spaces in which "$A \cap K$ is closed for all compact $K$" implies "$A$ is closed."
negative_passages.docid: 17733
negative_passages.text: $X$ second countable locally compact Hausdorff implies $C(X)$ separable?
negative_passages.docid: 59289
negative_passages.text: Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
negative_passages.docid: 73154
negative_passages.text: Compact subset in colimit of spaces
negative_passages.docid: 33140
negative_passages.text: Two non-homeomorphic spaces with continuous bijective functions in both directions
negative_passages.docid: 95993
negative_passages.text: Isn't every subset of a compact space compact?
negative_passages.docid: 131890
negative_passages.text: Totally disconnected space that is not $T_2$
negative_passages.docid: 156304
negative_passages.text: Prob 12, Sec 26 in Munkres' TOPOLOGY, 2nd ed: How to show that the domain of a perfect map is compact if its range is compact?
negative_passages.docid: 45249
negative_passages.text: Pseudocompactness does not imply compactness
negative_passages.docid: 64375
negative_passages.text: Non-Metrizable Topological Spaces
negative_passages.docid: 70017
negative_passages.text: Every subspace of a compact space is compact?