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Featured researches published by Petr Simon.


Topology and its Applications | 1991

On minimal π-character of points in extremally disconnected compact spaces

Bohuslav Balcar; Petr Simon

Abstract We consider the relationship between π-character, refinement number (=weak density) and π-weight in complete Boolean algebras. As an application we shall show that every extremally disconnected compact space contains a point which is not an accumulation point of any countable discrete subset, provided that minimal π-character and π-weight coincide.


Topology and its Applications | 2004

Spaces which are generated by discrete sets

Angelo Bella; Petr Simon

Abstract Continuing the study initiated by Dow, Tkachenko, Tkachuk and Wilson, we prove that countably compact countably tight spaces, normed linear spaces in the weak topology and function spaces over σ-compact spaces are discretely generated. We also construct, using [CH], a compact pseudoradial space and a pseudocompact space of countable tightness which are not discretely generated.


arXiv: General Topology | 2007

On the Pytkeev property in spaces of continuous functions

Petr Simon; Boaz Tsaban

Answering a question of Sakai, we show that the minimal cardi- nality of a set of reals X such that Cp(X) does not have the Pytkeev property is equal to the pseudo-intersection number p. Our approach leads to a natu- ral characterization of the Pytkeev property of Cp(X) by means of a covering property of X, and to a similar result for the Reznichenko property of Cp(X).


Discrete Mathematics | 1992

Reaping number and p-character of Boolean algebras

Bohuslav Balcar; Petr Simon

For every Boolean algebra B the minimal π-character of an ultrafilter on B is at most 2r2, where r2 is the reaping number of B. An example of B is given for which r2(B)< min{πχ(U): U ϵ Ult(B)}.


Topology and its Applications | 2000

An α4 , not Fréchet product of α4 Fréchet spaces

Camillo Costantini; Petr Simon

Abstract We shall construct in ZFC two Frechet–Urysohn α 4 -spaces, the product of which is α 4 , but fails to be Frechet–Urysohn. This answers Noguras question from 1985.


Archive | 1997

Origins of Dimension Theory

Miroslav Katĕtov; Petr Simon

It is well-known that there are three dimension functions recognized today in general topology.


Topology and its Applications | 1988

Ultrafilters on ω and atoms in the lattice of uniformities II

J. Pelant; Jan Reiterman; V. Rödl; Petr Simon

Abstract Interaction between ultrafilters and uniformities on a countable set is investigated. Various ultrafilters are constructed such that atoms in the lattice of uniformities refining the corresponding ultrafilter uniformities have special properties.


Topology and its Applications | 2002

A countable dense-in-itself dense P-set☆

Petr Simon

Abstract We shall show that several rather familiar countable topological spaces are embedded as P-sets in their Cech–Stone compactifications.


Topology and its Applications | 1990

On spaces in which every bounded subset is Hausdorff

Eraldo Giuli; Petr Simon

Abstract The class of spaces in the title (denoted by Haus(e-comp )) is introduced and it is compared with other classes of weak Hausdorff spaces. An explicit description of the Haus(e-comp )- epimorphisms is given by means of a variation of Arhangelskii–Franklins compactly determined closure. It is shown that Haus(e-comp ) is not co-well-powered.


Open Problems in Topology II | 2007

Completely separable MAD families

Michael Hrušák; Petr Simon

Publisher Summary This chapter provides an overview of completely separable maximal almost disjoint (MAD) families. An infinite family A ⊆ [ w ] w is almost disjoint if any two of its distinct elements have finite intersection. A family A is said to be a MAD family if it is almost disjoint and for every X ∈ [ w ] w there is an A ∈ A such that A ∩ X is infinite. There are almost disjoint (hence also MAD) families of cardinality c and many MAD families with special combinatorial and/or topological properties can be constructed using set-theoretic assumptions like CH, MA or b = c . However, special MAD families are notoriously difficult to construct in ZFC alone. The reason being the lack of a device ensuring that a recursive construction of a MAD family would not prematurely terminate, an object that would serve a similar purpose as independent linked families do for the construction of special ultra-filters. The notion of a completely separable MAD family is a candidate for such a device and is an interesting notion in its own right.

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Bohuslav Balcar

Charles University in Prague

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Alan Dow

University of North Carolina at Charlotte

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Florence Goutail

Centre national de la recherche scientifique

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Jerry E. Vaughan

University of North Carolina at Greensboro

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Michael Hrušák

National Autonomous University of Mexico

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J.-F. Müller

Belgian Institute for Space Aeronomy

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J.-P. Pommereau

Centre national de la recherche scientifique

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