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On meager function spaces, network character and meager convergence in topological spaces

Taras O. Banakh, Volodymyr Mykhaylyuk, Lubomyr Zdomsky (2011)

Commentationes Mathematicae Universitatis Carolinae

For a non-isolated point x of a topological space X let nw χ ( x ) be the smallest cardinality of a family 𝒩 of infinite subsets of X such that each neighborhood O ( x ) X of x contains a set N 𝒩 . We prove that (a) each infinite compact Hausdorff space X contains a non-isolated point x with nw χ ( x ) = 0 ; (b) for each point x X with nw χ ( x ) = 0 there is an injective sequence ( x n ) n ω in X that -converges to x for some meager filter on ω ; (c) if a functionally Hausdorff space X contains an -convergent injective sequence for some meager filter...

On n -in-countable bases

S. A. Peregudov (2000)

Commentationes Mathematicae Universitatis Carolinae

Some results concerning spaces with countably weakly uniform bases are generalized for spaces with n -in-countable ones.

On ( n , m ) - A -normal and ( n , m ) - A -quasinormal semi-Hilbertian space operators

Samir Al Mohammady, Sid Ahmed Ould Beinane, Sid Ahmed Ould Ahmed Mahmoud (2022)

Mathematica Bohemica

The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces, i.e. spaces generated by positive semi-definite sesquilinear forms. Let be a Hilbert space and let A be a positive bounded operator on . The semi-inner product h k A : = A h k , h , k , induces a semi-norm · A . This makes into a semi-Hilbertian space. An operator T A ( ) is said to be ( n , m ) - A -normal if [ T n , ( T A ) m ] : = T n ( T A ) m - ( T A ) m T n = 0 for some positive integers n and m .

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