Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science

2016-03-01

2016

Παπαδόπουλος Ιωάννης

Βασιλική Φαρμάκη Καθηγήτρια

Οι διατακτικοί αριθμοί και η δομή τους, αλγεβρική και τοπολογική

Greek

The voucher numbers and their structure, algebraic and topological

This dissertation centres on the algebraic and topological structure of ordinal
numbers. Initially, the ordinal numbers are defined and their basic properties
are proven, such as that they are well ordered sets, the class of all is not a
set, the nonzero marginal ordinal number exists and the transfinite induction
theorem.
By defining the well-ordered classes, the isomorf theorem among well-ordered
sets and ordinal numbers is proven as well as the fact that the class of all
the ordinal numbers is well ordered.
Furthermore, the properties of operations, the existence of a fixed point for
normal functional classes and Cantor’s normal form theorem is proven by
expanding the normal functions classes and defining the operations of addition,
multiplication and the powers of ordinal numbers.
By defining the topology layout as linear ordered sets, it is proven that every
ordinal number with such a topology layout is “Hausdorff” and a normal
topological space, while every subsequent is compact. The γ+1, γ, Ω+1, Ω
topological spaces with the aforementioned topology are studied thoroughly,
where Ω is the smallest uncountable ordinal number and γ marginally less than
Ω.
Finally, Tychonoff’s topological space is defined and proven that it is
pseudocompact, not normal and not sequentially compact even if it is an (open)
subspace of a compact and normal topological space.

Ordinal Numbers, The Isomorf Theorem , Functional Classes, Normal functions classes, Cantor’s Normal Form Theorem

No

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15

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File access is restricted.

https://pergamos.lib.uoa.gr/uoa/dl/object/1319234