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Metric-fine uniform frames

Joanne L. Walters-Wayland (1998)

Commentationes Mathematicae Universitatis Carolinae

A locallic version of Hager’s metric-fine spaces is presented. A general definition of 𝒜 -fineness is given and various special cases are considered, notably 𝒜 = all metric frames, 𝒜 = complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.

Monotone meta-Lindelöf spaces

Yin-Zhu Gao, Wei-Xue Shi (2009)

Czechoslovak Mathematical Journal

In this paper, we study the monotone meta-Lindelöf property. Relationships between monotone meta-Lindelöf spaces and other spaces are investigated. Behaviors of monotone meta-Lindelöf G O -spaces in their linearly ordered extensions are revealed.

Monotone weak Lindelöfness

Maddalena Bonanzinga, Filippo Cammaroto, Bruno Pansera (2011)

Open Mathematics

The definition of monotone weak Lindelöfness is similar to monotone versions of other covering properties: X is monotonically weakly Lindelöf if there is an operator r that assigns to every open cover U a family of open sets r(U) so that (1) ∪r(U) is dense in X, (2) r(U) refines U, and (3) r(U) refines r(V) whenever U refines V. Some examples and counterexamples of monotonically weakly Lindelöf spaces are given and some basic properties such as the behavior with respect to products and subspaces...

More about spaces with a small diagonal

Alan Dow, Oleg Pavlov (2006)

Fundamenta Mathematicae

Hušek defines a space X to have a small diagonal if each uncountable subset of X² disjoint from the diagonal has an uncountable subset whose closure is disjoint from the diagonal. Hušek proved that a compact space of weight ω₁ which has a small diagonal will be metrizable, but it remains an open problem to determine if the weight restriction is necessary. It has been shown to be consistent that each compact space with a small diagonal is metrizable; in particular, Juhász and Szentmiklóssy proved...

N-compact frames

Greg M. Schlitt (1991)

Commentationes Mathematicae Universitatis Carolinae

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

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 ℝ -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.

Normal subspaces in products of two ordinals

Nobuyuki Kemoto, Tsugunori Nogura, Kerry Smith, Yukinobu Yajima (1996)

Fundamenta Mathematicae

Let λ be an ordinal number. It is shown that normality, collectionwise normality and shrinking are equivalent for all subspaces of ( λ + 1 ) 2 .

Currently displaying 161 – 180 of 477