On topologies in the family of sets with the Baire property

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Jacek Hejduk
Keyword(s):  
Baire Space ◽  
Baire Property ◽  
The Family

AbstractStarting with an operator defined on the family of open sets in a topological Baire space

scholarly journals Note on limits of simply continuous and cliquish functions

1994 ◽  
Vol 17 (3) ◽  
pp. 447-450 ◽  
Author(s):  
Janina Ewert
Keyword(s):  
Metric Space ◽  
Continuous Functions ◽  
Baire Space ◽  
Baire Property ◽  
Baire Class ◽  
Class 1 ◽  
Pointwise Limit ◽  
Separable Metric Space

The main result of this paper is that any functionfdefined on a perfect Baire space(X,T)with values in a separable metric spaceYis cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence{fn:n≥1}of simply continuous functions. This result is obtained by a change of a topology onXand showing that a functionf:(X,T)→Yis cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.

THE BAIRE PROPERTY IN THE REMAINDERS OF SEMITOPOLOGICAL GROUPS

2013 ◽  
Vol 88 (2) ◽  
pp. 301-308 ◽  
Author(s):  
LI-HONG XIE ◽  
SHOU LIN
Keyword(s):  
Positive Answer ◽  
Baire Space ◽  
Baire Property ◽  
Topological Groups ◽  
Dichotomy Theorem ◽  
Semitopological Group

AbstractIt is proved that every remainder of a nonlocally compact semitopological group $G$ is a Baire space if and only if $G$ is not Čech-complete, which improves a dichotomy theorem of topological groups by Arhangel’skiǐ [‘The Baire property in remainders of topological groups and other results’, Comment. Math. Univ. Carolin. 50(2) (2009), 273–279], and also gives a positive answer to a question of Lin and Lin [‘About remainders in compactifications of paratopological groups’, ArXiv: 1106.3836v1 [Math. GN] 20 June 2011]. We also show that for a nonlocally compact rectifiable space $G$ every remainder of $G$ is either Baire, or meagre and Lindelöf.

scholarly journals On the regularity of topologies in the family of sets having the Baire property

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1291-1295 ◽  
Author(s):  
Jacek Hejduk
Keyword(s):  
Topological Space ◽  
Regularity Property ◽  
Baire Property ◽  
Proper Ideal ◽  
The Family ◽  
Meager Sets

The paper concerns the topologies introduced in the family of sets having the Baire property in a topological space (X, ?) and in the family generated by the sets having the Baire property and given a proper ?-ideal containing ? -meager sets. The regularity property of such topologies is investigated.

scholarly journals On Semiregularization of Some Abstract Density Topologies Involving Sets Having The Baire Property

2016 ◽  
Vol 65 (1) ◽  
pp. 37-48
Author(s):  
Jacek Hejduk ◽  
Renata Wiertelak ◽  
Wojciech Wojdowski
Keyword(s):  
Real Line ◽  
Baire Space ◽  
Baire Property ◽  
Density Topology ◽  
The Real ◽  
Real Functions

Abstract Some kind of abstract density topology in a topological Baire space is considered. The semiregularization of this type of topology on the real line in many cases is the coarsest topology for which real functions continuous with respect to the abstract density topology are continuous.

scholarly journals Comparison of Some Subfamilies of Functions Having The Baire Property

2016 ◽  
Vol 65 (1) ◽  
pp. 151-159
Author(s):  
Gertruda Ivanova ◽  
Aleksandra Karasińska ◽  
Elżbieta Wagner-Bojakowska
Keyword(s):  
Continuous Functions ◽  
Baire Property ◽  
Porous Set ◽  
Darboux Property ◽  
Darboux Functions ◽  
The Family

Abstract We prove that the family Q of quasi-continuous functions is a strongly porous set in the space Ba of functions having the Baire property. Moreover, the family DQ of all Darboux quasi-continuous functions is a strongly porous set in the space DBa of Darboux functions having the Baire property. It implies that each family of all functions having the A-Darboux property is strongly porous in DBa if A has the (∗)-property.

Porous subsets in the space of functions having the Baire property

2017 ◽  
Vol 67 (6) ◽  
Author(s):  
Gertruda Ivanova ◽  
Elżbieta Wagner-Bojakowska
Keyword(s):  
Real Line ◽  
Continuous Functions ◽  
Baire Property ◽  
The Real ◽  
Porous Set ◽  
The Family

AbstractThe comparison of some subfamilies of the family of functions on the real line having the Baire property in porosity terms is given. We prove that the family of all quasi-continuous functions is strongly porous set in the family of all cliquish functions and that the family of all cliquish functions is strongly porous set in the family of all functions having the Baire property.We prove also that the family of all Świątkowski functions is lower 2/3-porous set in the family of cliquish functions and the family of functions having the internally Świątkowski property is lower 2/3-porous set in the family of cliquish functions.

On topologies generated by some operators

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Katarzyna Flak ◽  
Jacek Hejduk
Keyword(s):  
Topological Space ◽  
Baire Property ◽  
Density Operators ◽  
The Family ◽  
Meager Sets

AbstractThe paper concerns topologies introduced in a topological space (X, τ) by operators which are much weaker than the lower density operators. Some properties of the family of sets having the Baire property and the family of meager sets with respect to such topologies are investigated.

Triassic sponges (Sphinctozoa) from Hells Canyon, Oregon

1988 ◽  
Vol 62 (03) ◽  
pp. 419-423 ◽  
Author(s):  
Baba Senowbari-Daryan ◽  
George D. Stanley
Keyword(s):  
Endemic Species ◽  
Upper Triassic ◽  
Island Arc ◽  
Tropical Island ◽  
The Family ◽  
Wallowa Terrane ◽  
Unique Condition ◽  
Hells Canyon

Two Upper Triassic sphinctozoan sponges of the family Sebargasiidae were recovered from silicified residues collected in Hells Canyon, Oregon. These sponges areAmblysiphonellacf.A. steinmanni(Haas), known from the Tethys region, andColospongia whalenin. sp., an endemic species. The latter sponge was placed in the superfamily Porata by Seilacher (1962). The presence of well-preserved cribrate plates in this sponge, in addition to pores of the chamber walls, is a unique condition never before reported in any porate sphinctozoans. Aporate counterparts known primarily from the Triassic Alps have similar cribrate plates but lack the pores in the chamber walls. The sponges from Hells Canyon are associated with abundant bivalves and corals of marked Tethyan affinities and come from a displaced terrane known as the Wallowa Terrane. It was a tropical island arc, suspected to have paleogeographic relationships with Wrangellia; however, these sponges have not yet been found in any other Cordilleran terrane.

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