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Mathematics Subject Classification – MSC2010

54-XX

General topology [For the topology of manifolds of all dimensions, see 57Nxx] 72055

54-00

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

54-01

Instructional exposition (textbooks, tutorial papers, etc.) 518

54-02

Research exposition (monographs, survey articles) 614

54-03

Historical (must also be assigned at least one classification number from Section 01) 339

54-04

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

54-06

Proceedings, conferences, collections, etc. 506

54Axx

Generalities 15263

54A05

Topological spaces and generalizations (closure spaces, etc.) 3145

54A10

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 1566

54A15

Syntopogeneous structures 125

54A20

Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 2381

54A25

Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] [For ultrafilters, see 54D80] 2574

54A35

Consistency and independence results [See also 03E35] 931

54A40

Fuzzy topology [See also 03E72] 5796

54A99

None of the above, but in this section 350

54Bxx

Basic constructions 8108

54B05

Subspaces 583

54B10

Product spaces 2211

54B15

Quotient spaces, decompositions 811

54B17

Adjunction spaces and similar constructions 88

54B20

Hyperspaces 2100

54B30

Categorical methods [See also 18B30] 1890

54B35

Spectra 705

54B40

Presheaves and sheaves [See also 18F20] 105

54B99

None of the above, but in this section 253

54Cxx

Maps and general types of spaces defined by maps 19741

54C05

Continuous maps 1727

54C08

Weak and generalized continuity 2573

54C10

Special maps on topological spaces (open, closed, perfect, etc.) 4038

54C15

Retraction 406

54C20

Extension of maps 1028

54C25

Embedding 699

54C30

Real-valued functions [See also 26-XX] 1281

54C35

Function spaces [See also 46Exx, 58D15] 2585

54C40

Algebraic properties of function spaces [See also 46J10] 813

54C45

$C$- and $C^*$-embedding 273

54C50

Special sets defined by functions [See also 26A21] 560

54C55

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 1183

54C56

Shape theory [See also 55P55, 57N25] 717

54C60

Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 4223

54C65

Selections [See also 28B20] 1133

54C70

Entropy 570

54C99

None of the above, but in this section 409

54Dxx

Fairly general properties 15426

54D05

Connected and locally connected spaces (general aspects) 1471

54D10

Lower separation axioms ($T_0$--$T_3$, etc.) 2128

54D15

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 1910

54D20

Noncompact covering properties (paracompact, Lindelöf, etc.) 3691

54D25

“$P$-minimal” and “$P$-closed” spaces 508

54D30

Compactness 3059

54D35

Extensions of spaces (compactifications, supercompactifications, completions, etc.) 2830

54D40

Remainders 570

54D45

Local compactness, $\sigma$-compactness 586

54D50

$k$-spaces 422

54D55

Sequential spaces 789

54D60

Realcompactness and realcompactification 508

54D65

Separability 393

54D70

Base properties 218

54D80

Special constructions of spaces (spaces of ultrafilters, etc.) 421

54D99

None of the above, but in this section 531

54Exx

Spaces with richer structures 15663

54E05

Proximity structures and generalizations 795

54E15

Uniform structures and generalizations 2704

54E17

Nearness spaces 265

54E18

$p$-spaces, $M$-spaces, $\sigma$-spaces, etc. 419

54E20

Stratifiable spaces, cosmic spaces, etc. 605

54E25

Semimetric spaces 306

54E30

Moore spaces 502

54E35

Metric spaces, metrizability 4557

54E40

Special maps on metric spaces 2514

54E45

Compact (locally compact) metric spaces 812

54E50

Complete metric spaces 1479

54E52

Baire category, Baire spaces 1117

54E55

Bitopologies 1192

54E70

Probabilistic metric spaces 793

54E99

None of the above, but in this section 743

54Fxx

Special properties 8616

54F05

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 2106

54F15

Continua and generalizations 2934

54F35

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

54F45

Dimension theory [See also 55M10] 2327

54F50

Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03] 1099

54F55

Unicoherence, multicoherence 221

54F65

Topological characterizations of particular spaces 792

54F99

None of the above, but in this section 312

54Gxx

Peculiar spaces 2294

54G05

Extremally disconnected spaces, $F$-spaces, etc. 685

54G10

$P$-spaces 191

54G12

Scattered spaces 222

54G15

Pathological spaces 185

54G20

Counterexamples 1002

54G99

None of the above, but in this section 164

54Hxx

Connections with other structures, applications 23945

54H05

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 1517

54H10

Topological representations of algebraic systems [See also 22-XX] 388

54H11

Topological groups [See also 22A05] 1232

54H12

Topological lattices, etc. [See also 06B30, 06F30] 392

54H13

Topological fields, rings, etc. [See also 12Jxx] [For algebraic aspects, see 13Jxx, 16W80] 320

54H15

Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx] 1409

54H20

Topological dynamics [See also 28Dxx, 37Bxx] 5188

54H25

Fixed-point and coincidence theorems [See also 47H10, 55M20] 13583

54H99

None of the above, but in this section 448

54Jxx

Nonstandard topology [See also 03H05] 281

54J05

Nonstandard topology [See also 03H05] 277

54J99

None of the above, but in this section 4

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Mathematics Subject Classification – MSC2010

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