16 research outputs found
Weak covering properties and selection principles
No convenient internal characterization of spaces that are productively
Lindelof is known. Perhaps the best general result known is Alster's internal
characterization, under the Continuum Hypothesis, of productively Lindelof
spaces which have a basis of cardinality at most . It turns out that
topological spaces having Alster's property are also productively weakly
Lindelof. The weakly Lindelof spaces form a much larger class of spaces than
the Lindelof spaces. In many instances spaces having Alster's property satisfy
a seemingly stronger version of Alster's property and consequently are
productively X, where X is a covering property stronger than the Lindelof
property. This paper examines the question: When is it the case that a space
that is productively X is also productively Y, where X and Y are covering
properties related to the Lindelof property.Comment: 16 page
Algebraic properties of generalized Rijndael-like ciphers
We provide conditions under which the set of Rijndael functions considered as
permutations of the state space and based on operations of the finite field
\GF (p^k) ( a prime number) is not closed under functional
composition. These conditions justify using a sequential multiple encryption to
strengthen the AES (Rijndael block cipher with specific block sizes) in case
AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R.
Wernsdorf provided conditions under which the group generated by the
Rijndael-like round functions based on operations of the finite field \GF
(2^k) is equal to the alternating group on the state space. In this paper we
provide conditions under which the group generated by the Rijndael-like round
functions based on operations of the finite field \GF (p^k) () is
equal to the symmetric group or the alternating group on the state space.Comment: 22 pages; Prelim0
The combinatorics of the Baer-Specker group
Denote the integers by Z and the positive integers by N.
The groups Z^k (k a natural number) are discrete, and the classification up
to isomorphism of their (topological) subgroups is trivial. But already for the
countably infinite power Z^N of Z, the situation is different. Here the product
topology is nontrivial, and the subgroups of Z^N make a rich source of examples
of non-isomorphic topological groups. Z^N is the Baer-Specker group.
We study subgroups of the Baer-Specker group which possess group theoretic
properties analogous to properties introduced by Menger (1924), Hurewicz
(1925), Rothberger (1938), and Scheepers (1996). The studied properties were
introduced independently by Ko\v{c}inac and Okunev. We obtain purely
combinatorial characterizations of these properties, and combine them with
other techniques to solve several questions of Babinkostova, Ko\v{c}inac, and
Scheepers.Comment: To appear in IJ
Some new directions in infinite-combinatorial topology
We give a light introduction to selection principles in topology, a young
subfield of infinite-combinatorial topology. Emphasis is put on the modern
approach to the problems it deals with. Recent results are described, and open
problems are stated. Some results which do not appear elsewhere are also
included, with proofs.Comment: Small update
The development of sustainable lime-based building wall components
EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Selective Versions of \u3cem\u3eθ\u3c/em\u3e-Density
In [3] the authors initiate the study of selective versions of the notion of θ-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising in the set theory of the real line, and game-theoretic assertions regarding θ-separability