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Mathematics Subject Classification – MSC2010

54-XX

General topology [For the topology of manifolds of all dimensions, see 57Nxx] 72908

54-00

General reference works (handbooks, dictionaries, bibliographies, etc.) 26

54-01

Instructional exposition (textbooks, tutorial papers, etc.) 520

54-02

Research exposition (monographs, survey articles) 617

54-03

Historical (must also be assigned at least one classification number from Section 01) 341

54-04

Explicit machine computation and programs (not the theory of computation or programming) 18

54-06

Proceedings, conferences, collections, etc. 508

54Axx

Generalities 15509

54A05

Topological spaces and generalizations (closure spaces, etc.) 3187

54A10

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 1580

54A15

Syntopogeneous structures 126

54A20

Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 2411

54A25

Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] [For ultrafilters, see 54D80] 2590

54A35

Consistency and independence results [See also 03E35] 941

54A40

Fuzzy topology [See also 03E72] 5963

54A99

None of the above, but in this section 352

54Bxx

Basic constructions 8171

54B05

Subspaces 594

54B10

Product spaces 2231

54B15

Quotient spaces, decompositions 812

54B17

Adjunction spaces and similar constructions 89

54B20

Hyperspaces 2120

54B30

Categorical methods [See also 18B30] 1901

54B35

Spectra 706

54B40

Presheaves and sheaves [See also 18F20] 106

54B99

None of the above, but in this section 257

54Cxx

Maps and general types of spaces defined by maps 19914

54C05

Continuous maps 1763

54C08

Weak and generalized continuity 2599

54C10

Special maps on topological spaces (open, closed, perfect, etc.) 4066

54C15

Retraction 408

54C20

Extension of maps 1032

54C25

Embedding 700

54C30

Real-valued functions [See also 26-XX] 1295

54C35

Function spaces [See also 46Exx, 58D15] 2609

54C40

Algebraic properties of function spaces [See also 46J10] 822

54C45

$C$- and $C^*$-embedding 274

54C50

Special sets defined by functions [See also 26A21] 563

54C55

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 1185

54C56

Shape theory [See also 55P55, 57N25] 721

54C60

Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 4278

54C65

Selections [See also 28B20] 1143

54C70

Entropy 572

54C99

None of the above, but in this section 412

54Dxx

Fairly general properties 15551

54D05

Connected and locally connected spaces (general aspects) 1486

54D10

Lower separation axioms ($T_0$--$T_3$, etc.) 2156

54D15

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 1928

54D20

Noncompact covering properties (paracompact, Lindelöf, etc.) 3713

54D25

“$P$-minimal” and “$P$-closed” spaces 509

54D30

Compactness 3093

54D35

Extensions of spaces (compactifications, supercompactifications, completions, etc.) 2847

54D40

Remainders 574

54D45

Local compactness, $\sigma$-compactness 590

54D50

$k$-spaces 423

54D55

Sequential spaces 791

54D60

Realcompactness and realcompactification 510

54D65

Separability 400

54D70

Base properties 220

54D80

Special constructions of spaces (spaces of ultrafilters, etc.) 430

54D99

None of the above, but in this section 531

54Exx

Spaces with richer structures 15942

54E05

Proximity structures and generalizations 805

54E15

Uniform structures and generalizations 2714

54E17

Nearness spaces 263

54E18

$p$-spaces, $M$-spaces, $\sigma$-spaces, etc. 420

54E20

Stratifiable spaces, cosmic spaces, etc. 609

54E25

Semimetric spaces 310

54E30

Moore spaces 505

54E35

Metric spaces, metrizability 4634

54E40

Special maps on metric spaces 2645

54E45

Compact (locally compact) metric spaces 824

54E50

Complete metric spaces 1518

54E52

Baire category, Baire spaces 1127

54E55

Bitopologies 1206

54E70

Probabilistic metric spaces 810

54E99

None of the above, but in this section 746

54Fxx

Special properties 8671

54F05

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 2137

54F15

Continua and generalizations 2943

54F35

Higher-dimensional local connectedness [See also 55Mxx, 55Nxx] 102

54F45

Dimension theory [See also 55M10] 2334

54F50

Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03] 1101

54F55

Unicoherence, multicoherence 221

54F65

Topological characterizations of particular spaces 800

54F99

None of the above, but in this section 312

54Gxx

Peculiar spaces 2311

54G05

Extremally disconnected spaces, $F$-spaces, etc. 688

54G10

$P$-spaces 192

54G12

Scattered spaces 224

54G15

Pathological spaces 187

54G20

Counterexamples 1011

54G99

None of the above, but in this section 165

54Hxx

Connections with other structures, applications 24326

54H05

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 1532

54H10

Topological representations of algebraic systems [See also 22-XX] 393

54H11

Topological groups [See also 22A05] 1246

54H12

Topological lattices, etc. [See also 06B30, 06F30] 393

54H13

Topological fields, rings, etc. [See also 12Jxx] [For algebraic aspects, see 13Jxx, 16W80] 322

54H15

Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx] 1421

54H20

Topological dynamics [See also 28Dxx, 37Bxx] 5254

54H25

Fixed-point and coincidence theorems [See also 47H10, 55M20] 13849

54H99

None of the above, but in this section 451

54Jxx

Nonstandard topology [See also 03H05] 282

54J05

Nonstandard topology [See also 03H05] 278

54J99

None of the above, but in this section 4

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Mathematics Subject Classification – MSC2010

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