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28 relations: Baire category theorem, Bijection, Cecilia Krieger, Closed set, Disjoint sets, General topology, Georg Cantor, Gδ set, Graduate Texts in Mathematics, Homeomorphism, Induced topology, Isolated point, Limit ordinal, Limit point, Mathematics, Ordinal number, Perfect set, Perfect set property, Polish space, Real line, Separated sets, Set theory, T1 space, Topological space, Topology, Transfinite induction, University of Toronto, Wacław Sierpiński.
Baire category theorem
The Baire category theorem (BCT) is an important tool in general topology and functional analysis.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Cecilia Krieger
Cypra Cecilia Krieger-Dunaij (9 April 1894 – 17 August 1974) was an Austro-Hungarian (more specifically, Galician)-born mathematician of Jewish ancestry who lived and worked in Canada.
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Closed set
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Gδ set
In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets.
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Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.
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Homeomorphism
In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.
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Induced topology
In topology and related areas of mathematics, an induced topology on a topological space is a topology which makes the inducing function continuous from/to this topological space.
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Isolated point
In mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S but there exists a neighborhood of x which does not contain any other points of S. This is equivalent to saying that the singleton is an open set in the topological space S (considered as a subspace of X).
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Limit ordinal
In set theory, a limit ordinal is an ordinal number that is neither zero nor a successor ordinal.
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Limit point
In mathematics, a limit point (or cluster point or accumulation point) of a set S in a topological space X is a point x that can be "approximated" by points of S in the sense that every neighbourhood of x with respect to the topology on X also contains a point of S other than x itself.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Ordinal number
In set theory, an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a collection of objects in order, one after another.
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Perfect set
In mathematics, in the field of topology, a subset of a topological space is perfect if it is closed and has no isolated points.
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Perfect set property
In descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset (Kechris 1995, p. 150).
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Polish space
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Separated sets
In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way: roughly speaking, neither overlapping nor touching.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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T1 space
In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other.
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Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods.
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Topology
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.
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Transfinite induction
Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.
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University of Toronto
The University of Toronto (U of T, UToronto, or Toronto) is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen's Park.
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Wacław Sierpiński
Wacław Franciszek Sierpiński (14 March 1882 – 21 October 1969) was a Polish mathematician.
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Redirects here:
Bendixson derivative, Cantor-Bendixson derivative, Cantor–Bendixson derivative, Cantor–Bendixson rank, Perfect sets.
References
[1] https://en.wikipedia.org/wiki/Derived_set_(mathematics)
