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Mathematics Subject Classification – MSC2010

54-XX

General topology [For the topology of manifolds of all dimensions, see 57Nxx] 72427

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) 615

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. 507

54Axx

Generalities 15337

54A05

Topological spaces and generalizations (closure spaces, etc.) 3172

54A10

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 1571

54A15

Syntopogeneous structures 125

54A20

Convergence in general topology (sequences, filters, limits, convergence spaces, etc.) 2392

54A25

Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] [For ultrafilters, see 54D80] 2581

54A35

Consistency and independence results [See also 03E35] 935

54A40

Fuzzy topology [See also 03E72] 5834

54A99

None of the above, but in this section 351

54Bxx

Basic constructions 8142

54B05

Subspaces 586

54B10

Product spaces 2219

54B15

Quotient spaces, decompositions 812

54B17

Adjunction spaces and similar constructions 89

54B20

Hyperspaces 2111

54B30

Categorical methods [See also 18B30] 1900

54B35

Spectra 705

54B40

Presheaves and sheaves [See also 18F20] 105

54B99

None of the above, but in this section 254

54Cxx

Maps and general types of spaces defined by maps 19819

54C05

Continuous maps 1736

54C08

Weak and generalized continuity 2587

54C10

Special maps on topological spaces (open, closed, perfect, etc.) 4049

54C15

Retraction 407

54C20

Extension of maps 1031

54C25

Embedding 700

54C30

Real-valued functions [See also 26-XX] 1288

54C35

Function spaces [See also 46Exx, 58D15] 2597

54C40

Algebraic properties of function spaces [See also 46J10] 819

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] 1185

54C56

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

54C60

Set-valued maps [See also 26E25, 28B20, 47H04, 58C06] 4250

54C65

Selections [See also 28B20] 1137

54C70

Entropy 570

54C99

None of the above, but in this section 410

54Dxx

Fairly general properties 15483

54D05

Connected and locally connected spaces (general aspects) 1475

54D10

Lower separation axioms ($T_0$--$T_3$, etc.) 2140

54D15

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 1917

54D20

Noncompact covering properties (paracompact, Lindelöf, etc.) 3706

54D25

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

54D30

Compactness 3071

54D35

Extensions of spaces (compactifications, supercompactifications, completions, etc.) 2840

54D40

Remainders 572

54D45

Local compactness, $\sigma$-compactness 587

54D50

$k$-spaces 423

54D55

Sequential spaces 790

54D60

Realcompactness and realcompactification 508

54D65

Separability 396

54D70

Base properties 218

54D80

Special constructions of spaces (spaces of ultrafilters, etc.) 427

54D99

None of the above, but in this section 531

54Exx

Spaces with richer structures 15763

54E05

Proximity structures and generalizations 798

54E15

Uniform structures and generalizations 2707

54E17

Nearness spaces 265

54E18

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

54E20

Stratifiable spaces, cosmic spaces, etc. 606

54E25

Semimetric spaces 310

54E30

Moore spaces 505

54E35

Metric spaces, metrizability 4585

54E40

Special maps on metric spaces 2559

54E45

Compact (locally compact) metric spaces 815

54E50

Complete metric spaces 1494

54E52

Baire category, Baire spaces 1119

54E55

Bitopologies 1197

54E70

Probabilistic metric spaces 801

54E99

None of the above, but in this section 744

54Fxx

Special properties 8637

54F05

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 2118

54F15

Continua and generalizations 2938

54F35

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

54F45

Dimension theory [See also 55M10] 2329

54F50

Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03] 1100

54F55

Unicoherence, multicoherence 221

54F65

Topological characterizations of particular spaces 795

54F99

None of the above, but in this section 312

54Gxx

Peculiar spaces 2301

54G05

Extremally disconnected spaces, $F$-spaces, etc. 687

54G10

$P$-spaces 192

54G12

Scattered spaces 223

54G15

Pathological spaces 185

54G20

Counterexamples 1006

54G99

None of the above, but in this section 164

54Hxx

Connections with other structures, applications 24122

54H05

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 1521

54H10

Topological representations of algebraic systems [See also 22-XX] 391

54H11

Topological groups [See also 22A05] 1233

54H12

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

54H13

Topological fields, rings, etc. [See also 12Jxx] [For algebraic aspects, see 13Jxx, 16W80] 321

54H15

Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx] 1417

54H20

Topological dynamics [See also 28Dxx, 37Bxx] 5221

54H25

Fixed-point and coincidence theorems [See also 47H10, 55M20] 13712

54H99

None of the above, but in this section 449

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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