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Factorization theorems for strong maps between matroids of arbitrary cardinality

100%
Mao H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
687-692
EN
In this paper we present factorization theorems for strong maps between matroids of arbitrary cardinality. Moreover, we present a new way to prove the factorization theorem for strong maps between finite matroids.
2
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Ordinal ultrafilters versus P-hierarchy

76%
Starosolski A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
84-96
EN
An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.
3
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Ideals which generalize (v 0)

76%
Kalemba P., Plewik S.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1016-1025
EN
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
4
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Topological spaces compact with respect to a set of filters

64%
Lipparini P.
Open Mathematics
|
2014
|
tom 12
|
nr 7
991-999
EN
If is a family of filters over some set I, a topological space X is sequencewise -compact if for every I-indexed sequence of elements of X there is such that the sequence has an F-limit point. Countable compactness, sequential compactness, initial κ-compactness, [λ; µ]-compactness, the Menger and Rothberger properties can all be expressed in terms of sequencewise -compactness for appropriate choices of . We show that sequencewise -compactness is preserved under taking products if and only if there is a filter such that sequencewise -compactness is equivalent to F-compactness. If this is the case, and there exists a sequencewise -compact T 1 topological space with more than one point, then F is necessarily an ultrafilter. The particular case of sequential compactness is analyzed in detail.
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