PTOP:010117Cofinite opens force infinite sets dense and kill Hausdorff separationView problem statementCofinite Topology AxiomsCofinite Closure Compactness SeparationTopological spaces, bases, subbases, and neighborhood systemsPoint-Set Topology · Mixed review—
PTOP:010118Dictionary order and the plane subspace topology are incomparableView access optionsOrder Topology Basis ComparisonDictionary Order Subspace MismatchTopological spaces, bases, subbases, and neighborhood systemsPoint-Set Topology · Mixed review—
PTOP:010219The diagonal breaks in the box topology, but addition survivesView access optionsBox Versus Product TopologyDiagonal Failure Box Addition Continuity AuditContinuity, initial topologies, products, and netsPoint-Set Topology · Mixed review—
PTOP:010220Finite closed pasting works; a countable closed cover can failView access optionsFinite Closed Pasting LemmaInfinite Closed Cover Pasting FailureContinuity, initial topologies, products, and netsPoint-Set Topology · Mixed review—
PTOP:010321A quotient of a compact Hausdorff space is Hausdorff exactly when the relation is closedView access optionsClosed Relation Quotient HausdorffEndpoint Identification CircleQuotient spaces, identification maps, and universal descentPoint-Set Topology · Mixed review—
PTOP:010422Regular plus Lindelöf yields normality by countable shrinkingView access optionsRegular Lindelof Normal ProofCountable Shrinking OF CoversSeparation and countability axiomsPoint-Set Topology · Mixed review—
PTOP:010523One-point compactification is Hausdorff exactly for locally compact Hausdorff spacesView access optionsOne Point Compactification TopologyLocal Compactness Hausdorff CriterionCompactness, local compactness, and compactificationPoint-Set Topology · Mixed review—
PTOP:010524Compact Hausdorff spaces are normal by closed-neighborhood shrinkingView access optionsCompact Hausdorff RegularityCompact Hausdorff NormalityCompactness, local compactness, and compactificationPoint-Set Topology · Mixed review—
PTOP:010525First countability turns compact cluster points into subsequencesView access optionsCompact First Countable SequentialProduct Compact Not Sequentially CompactCompactness, local compactness, and compactificationPoint-Set Topology · Mixed review—
PTOP:010626The topologist's comb is path connected yet not locally connectedView access optionsPath Connectedness OF CombLocal Connectedness Failure AT Limit ToothConnectedness, path connectedness, and componentsPoint-Set Topology · Mixed review—