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Special almost P-spaces

Alessandro Fedeli — 1997

Commentationes Mathematicae Universitatis Carolinae

Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space X of this kind the inequality “ | X | ψ c ( X ) t ( X ) " holds.

Two cardinal inequalities for functionally Hausdorff spaces

Alessandro Fedeli — 1994

Commentationes Mathematicae Universitatis Carolinae

In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the τ θ -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if X is a functionally Hausdorff space, then | X | 2 χ ( X ) wcd ( X ) .

On the cardinality of functionally Hausdorff spaces

Alessandro Fedeli — 1996

Commentationes Mathematicae Universitatis Carolinae

In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If X is a functionally Hausdorff space then | X | 2 f s ( X ) ψ τ ( X ) ; (ii) Let X be a functionally Hausdorff space with f s ( X ) κ . Then there is a subset S of X such that | S | 2 κ and X = { c l τ θ ( A ) : A [ S ] κ } .

On the k -Baire property

Alessandro Fedeli — 1993

Commentationes Mathematicae Universitatis Carolinae

In this note we show the following theorem: “Let X be an almost k -discrete space, where k is a regular cardinal. Then X is k + -Baire iff it is a k -Baire space and every point- k open cover 𝒰 of X such that card ( 𝒰 ) k is locally- k at a dense set of points.” For k = 0 we obtain a well-known characterization of Baire spaces. The case k = 1 is also discussed.

ω H-sets and cardinal invariants

Alessandro Fedeli — 1998

Commentationes Mathematicae Universitatis Carolinae

A subset A of a Hausdorff space X is called an ω H-set in X if for every open family 𝒰 in X such that A 𝒰 there exists a countable subfamily 𝒱 of 𝒰 such that A { V ¯ : V 𝒱 } . In this paper we introduce a new cardinal function t s θ and show that | A | 2 t s θ ( X ) ψ c ( X ) for every ω H-set A of a Hausdorff space X .

On the cardinality of Hausdorff spaces

Alessandro Fedeli — 1998

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to show, using the reflection principle, three new cardinal inequalities. These results improve some well-known bounds on the cardinality of Hausdorff spaces.

An independency result in connectification theory

Alessandro FedeliAttilio Le Donne — 1999

Commentationes Mathematicae Universitatis Carolinae

A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 𝔠 clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither ψ nor ¬ ψ is provable in ZFC.

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