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Mathematics Subject Classification – MSC2020

54-XX

General topology {For the topology of manifolds of all dimensions, see 57Nxx} 76163

54-00

General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to general topology 26

54-01

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general topology 540

54-02

Research exposition (monographs, survey articles) pertaining to general topology 647

54-03

History of general topology [Consider also classification numbers pertaining to Section 01-XX] 351

54-04

Software, source code, etc. for problems pertaining to general topology 19

54-06

Proceedings, conferences, collections, etc. pertaining to general topology 522

54-08

Computational methods for problems pertaining to general topology 0

54-11

Research data for problems pertaining to general topology 0

54Axx

Generalities in topology 16214

54A05

Topological spaces and generalizations (closure spaces, etc.) 3421

54A10

Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 1653

54A15

Syntopogeneous structures 129

54A20

Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 2499

54A25

Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80} 2674

54A35

Consistency and independence results in general topology [See also 03E35] 987

54A40

Fuzzy topology [See also 03E72] 6236

54A99

None of the above, but in this section 358

54Bxx

Basic constructions in general topology 8407

54B05

Subspaces in general topology 620

54B10

Product spaces in general topology 2286

54B15

Quotient spaces, decompositions in general topology 837

54B17

Adjunction spaces and similar constructions in general topology 92

54B20

Hyperspaces in general topology 2185

54B30

Categorical methods in general topology [See also 18F60] 1953

54B35

Spectra in general topology 718

54B40

Presheaves and sheaves in general topology [See also 18F20] 112

54B99

None of the above, but in this section 267

54Cxx

Maps and general types of topological spaces defined by maps 20587

54C05

Continuous maps 1862

54C08

Weak and generalized continuity 2744

54C10

Special maps on topological spaces (open, closed, perfect, etc.) 4169

54C15

Retraction 417

54C20

Extension of maps 1062

54C25

Embedding 714

54C30

Real-valued functions in general topology [See also 26-XX] 1375

54C35

Function spaces in general topology [See also 46Exx, 58D15] 2714

54C40

Algebraic properties of function spaces in general topology [See also 46J10] 861

54C45

\(C\)- and \(C^*\)-embedding 282

54C50

Topology of special sets defined by functions [See also 26A21] 580

54C55

Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15] 1203

54C56

Shape theory in general topology [See also 55P55, 57N25] 731

54C60

Set-valued maps in general topology [See also 26E25, 28B20, 47H04, 58C06] 4425

54C65

Selections in general topology [See also 28B20] 1169

54C70

Entropy in general topology 581

54C99

None of the above, but in this section 422

54Dxx

Fairly general properties of topological spaces 16122

54D05

Connected and locally connected spaces (general aspects) 1547

54D10

Lower separation axioms (\(T_0\)–\(T_3\), etc.) 2272

54D15

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 1984

54D20

Noncompact covering properties (paracompact, Lindelöf, etc.) 3851

54D25

“\(P\)-minimal” and “\(P\)-closed” spaces 513

54D30

Compactness 3207

54D35

Extensions of spaces (compactifications, supercompactifications, completions, etc.) 2917

54D40

Remainders in general topology 598

54D45

Local compactness, \(\sigma\)-compactness 612

54D50

\(k\)-spaces 432

54D55

Sequential spaces 814

54D60

Realcompactness and realcompactification 516

54D65

Separability of topological spaces 412

54D70

Base properties of topological spaces 233

54D80

Special constructions of topological spaces (spaces of ultrafilters, etc.) 473

54D99

None of the above, but in this section 549

54Exx

Topological spaces with richer structures 16741

54E05

Proximity structures and generalizations 823

54E15

Uniform structures and generalizations 2777

54E17

Nearness spaces 266

54E18

\(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc. 427

54E20

Stratifiable spaces, cosmic spaces, etc. 621

54E25

Semimetric spaces 322

54E30

Moore spaces 511

54E35

Metric spaces, metrizability 4859

54E40

Special maps on metric spaces 2974

54E45

Compact (locally compact) metric spaces 837

54E50

Complete metric spaces 1659

54E52

Baire category, Baire spaces 1161

54E55

Bitopologies 1259

54E70

Probabilistic metric spaces 838

54E99

None of the above, but in this section 771

54Fxx

Special properties of topological spaces 8941

54F05

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 2241

54F15

Continua and generalizations 3023

54F16

Hyperspaces of continua 12

54F17

Inverse limits of set-valued functions 6

54F35

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

54F45

Dimension theory in general topology [See also 55M10] 2377

54F50

Topological spaces of dimension \(\leq 1\); curves, dendrites [See also 26A03] 1126

54F55

Unicoherence, multicoherence 228

54F65

Topological characterizations of particular spaces 833

54F99

None of the above, but in this section 315

54Gxx

Peculiar topological spaces 2404

54G05

Extremally disconnected spaces, \(F\)-spaces, etc. 716

54G10

\(P\)-spaces 204

54G12

Scattered spaces 239

54G15

Pathological topological spaces 192

54G20

Counterexamples in general topology 1044

54G99

None of the above, but in this section 175

54Hxx

Connections of general topology with other structures, applications 25725

54H05

Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 1581

54H10

Topological representations of algebraic systems [See also 22-XX] 405

54H11

Topological groups (topological aspects) [See also 22A05] 1372

54H12

Topological lattices, etc. (topological aspects) [See also 06B30, 06F30] 406

54H13

Topological fields, rings, etc. (topological aspects) [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80} 336

54H15

Transformation groups and semigroups (topological aspects) [See also 20M20, 22-XX, 57Sxx] 1450

54H25

Fixed-point and coincidence theorems (topological aspects) [See also 47H10, 55M20] 14828

54H30

Applications of general topology to computer science (e.g., digital topology, image processing) [See also 68U03] 2

54H99

None of the above, but in this section 467

54Jxx

Nonstandard topology [See also 03H05] 287

54J05

Nonstandard topology [See also 03H05] 283

54J99

None of the above, but in this section 4

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Mathematics Subject Classification – MSC2020

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