54-XX	General topology {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]
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]
54C40	Algebraic properties of function spaces [See also 46J10]
54C45	C- and C*-embedding
54C50	Special sets defined by functions [See also 26A21]
54C55	Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]
54C56	Shape theory [See also 55P55, 57N25]
54C60	Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
54C65	Selections [See also 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, (T0 - T3, etc.)
54D15	Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D20	Noncompact covering properties (paracompact, Lindel\"of, 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, partially ordered spaces, and partially ordered spaces [See also 06B30, 06F30]
54F15	Continua and generalizations
54F35	Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]
54F45	Dimension theory [See also 55M10]
54F50	Spaces of dimension \leq; 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]
54H10	Topological representations of algebraic systems [See also 22-XX]
54H11	Topological groups [See also 22A05]
54H12	Topological lattices, etc. [See also 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]
54H20	Topological dynamics [See also 28Dxx, 37Bxx]
54H25	Fixed-point and coincidence theorems [See also 47H10, 55M20]
54H99	None of the above, but in this section
54J05	Nonstandard topology [See also 03H05]