| 54-XX | | Prev: 53 | Up: Top | Next: 55 | |
| General topology [xref: 18B30] | |
| {For the topology of manifolds of all dimensions, see 57Nxx} |
54-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 54-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 54-02
| Research exposition (monographs, survey articles)
| 54-03
| Historical (must also be assigned at least one classification number from Section 01)
| 54-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 54-06
| Proceedings, conferences, collections, etc.
| |
54Axx
| Generalities
| 54A05 |
Topological spaces and generalizations (closure spaces, etc.)
| 54A10 |
Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
| 54A15 |
Syntopogeneous structures
| 54A20 |
Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
| 54A25 |
Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] {For ultrafilters, see 54D80}
| 54A35 |
Consistency and independence results [See also 03E35]
| 54A40 |
Fuzzy topology [See also 03E72]
| 54A99 |
None of the above, but in this section
| |
54Bxx
| Basic constructions
| 54B05 |
Subspaces
| 54B10 |
Product spaces
| 54B15 |
Quotient spaces, decompositions
| 54B17 |
Adjunction spaces and similar constructions
| 54B20 |
Hyperspaces
| 54B30 |
Categorical methods [See also 18B30]
| 54B35 |
Spectra
| 54B40 |
Presheaves and sheaves [See also 18F20]
[xref: 18F20]
| 54B99 |
None of the above, but in this section
| |
54Cxx
| Maps and general types of spaces defined by maps
| 54C05 |
Continuous maps
| 54C08 |
Weak and generalized continuity
| 54C10 |
Special maps on topological spaces (open, closed, perfect, etc.)
| 54C15 |
Retraction
| 54C20 |
Extension of maps
| 54C25 |
Embedding
| 54C30 |
Real-valued functions [See also 26-XX]
| 54C35 |
Function spaces [See also 46Exx, 58D15]
[xref: 58D15]
| 54C40 |
Algebraic properties of function spaces [See also 46J10]
| 54C45 |
$C$- and $C^*$-embedding
| 54C50 |
Special sets defined by functions [See also 26A21]
[xref: 26A21]
| 54C55 |
Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]
[xref: 55M15]
| 54C56 |
Shape theory [See also 55P55, 57N25]
[xref: 55P55, 57N25]
| 54C60 |
Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
[xref: 26E25, 28B20, 47H04, 49J53, 58C06]
| 54C65 |
Selections [See also 28B20]
[xref: 28B20]
| 54C70 |
Entropy
| 54C99 |
None of the above, but in this section
| |
54Dxx
| Fairly general properties
| 54D05 |
Connected and locally connected spaces (general aspects)
| 54D10 |
Lower separation axioms ($T_0$--$T_3$, etc.)
| 54D15 |
Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
| 54D20 |
Noncompact covering properties (paracompact, Lindelöf, etc.)
| 54D25 |
``$P$-minimal'' and ``$P$-closed'' spaces
| 54D30 |
Compactness
| 54D35 |
Extensions of spaces (compactifications, supercompactifications, completions, etc.)
| 54D40 |
Remainders
| 54D45 |
Local compactness, $\sigma$-compactness
| 54D50 |
$k$-spaces
| 54D55 |
Sequential spaces
| 54D60 |
Realcompactness and realcompactification
| 54D65 |
Separability
| 54D70 |
Base properties
| 54D80 |
Special constructions of spaces (spaces of ultrafilters, etc.)
| 54D99 |
None of the above, but in this section
| |
54Exx
| Spaces with richer structures
| 54E05 |
Proximity structures and generalizations
| 54E15 |
Uniform structures and generalizations
| 54E17 |
Nearness spaces
| 54E18 |
$p$-spaces, $M$-spaces, $\sigma$-spaces, etc.
| 54E20 |
Stratifiable spaces, cosmic spaces, etc.
| 54E25 |
Semimetric spaces
| 54E30 |
Moore spaces
| 54E35 |
Metric spaces, metrizability
| 54E40 |
Special maps on metric spaces
| 54E45 |
Compact (locally compact) metric spaces
| 54E50 |
Complete metric spaces
| 54E52 |
Baire category, Baire spaces
| 54E55 |
Bitopologies
| 54E70 |
Probabilistic metric spaces
| 54E99 |
None of the above, but in this section
| |
54Fxx
| Special properties
| 54F05 |
Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]
[xref: 06B30, 06F30]
| 54F15 |
Continua and generalizations
| 54F35 |
Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]
| 54F45 |
Dimension theory [See also 55M10]
[xref: 55M10]
| 54F50 |
Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
| 54F55 |
Unicoherence, multicoherence
| 54F65 |
Topological characterizations of particular spaces
| 54F99 |
None of the above, but in this section
| |
54Gxx
| Peculiar spaces
| 54G05 |
Extremally disconnected spaces, $F$-spaces, etc.
| 54G10 |
$P$-spaces
| 54G12 |
Scattered spaces
| 54G15 |
Pathological spaces
| 54G20 |
Counterexamples
| 54G99 |
None of the above, but in this section
| |
54Hxx
| Connections with other structures, applications
| 54H05 |
Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
[xref: 03E15, 28A05]
| 54H10 |
Topological representations of algebraic systems [See also 22-XX]
[xref: 28A60]
| 54H11 |
Topological groups [See also 22A05]
| 54H12 |
Topological lattices, etc. [See also 06B30, 06F30]
[xref: 06B30, 06F30]
| 54H13 |
Topological fields, rings, etc. [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80}
| 54H15 |
Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]
[xref: 20M20, 57Sxx]
| 54H20 |
Topological dynamics [See also 28Dxx, 37Bxx]
[xref: 28Dxx, 37Bxx, 46L55]
| 54H25 |
Fixed-point and coincidence theorems [See also 47H10, 55M20]
[xref: 26A18, 47H10, 55M20]
| 54H99 |
None of the above, but in this section
| |
54J05
| Nonstandard topology [See also 03H05]
[xref: 03H05, 26E35]
| |