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N-compact frames

Greg M. Schlitt (1991)

Commentationes Mathematicae Universitatis Carolinae

We investigate notions of -compactness for frames. We find that the analogues of equivalent conditions defining -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘ -cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial -compactness form a much larger class, and better embody what ‘ -compact frames’ should be. This latter property is expressible without reference...

Neighborhood spaces.

Kent, D.C., Min, Won Keun (2002)

International Journal of Mathematics and Mathematical Sciences

Network character and tightness of the compact-open topology

Richard N. Ball, Anthony W. Hager (2006)

Commentationes Mathematicae Universitatis Carolinae

For Tychonoff X and α an infinite cardinal, let α def X : = the minimum number of α  cozero-sets of the Čech-Stone compactification which intersect to X (generalizing -defect), and let rt X : = min α max ( α , α def X ) . Give C ( X ) the compact-open topology. It is shown that τ C ( X ) n χ C ( X ) rt X = max ( L ( X ) , L ( X ) def X ) , where: τ is tightness; n χ is the network character; L ( X ) is the Lindel"of number. For example, it follows that, for X Čech-complete, τ C ( X ) = L ( X ) . The (apparently new) cardinal functions n χ C and rt are compared with several others.

New properties of the concentric circle space and its applications to cardinal inequalities

Shu Hao Sun, Koo Guan Choo (1991)

Commentationes Mathematicae Universitatis Carolinae

It is well-known that the concentric circle space has no G δ -diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of G δ -diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.

Nilsystèmes d’ordre 2 et parallélépipèdes

Bernard Host, Alejandro Maass (2007)

Bulletin de la Société Mathématique de France

En topologie dynamique, une famille classique de systèmes est celle formée par les rotations minimales. La classe des nilsystèmes et de leurs limites projectives en est une extension naturelle. L’étude de ces systèmes est ancienne mais connaît actuellement un renouveau à cause de ses applications, à la fois à la théorie ergodique et en théorie additive des nombres. Les rotations minimales sont caractérisées par le fait que la relation de proximalité régionale est l’égalité. Nous introduisons une...

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