On the simplicity of some categories of closure spaces
Displaying 221 – 240 of 258
On the space of irrational numbers
Miroslav Katětov (1960)
Commentationes Mathematicae Universitatis Carolinae
On the structure of perfect sets in various topologies associated with tree forcings
Andrzej Nowik, Patrick Reardon (2013)
Open Mathematics
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
On the subsets of non locally compact points of ultracomplete spaces
Iwao Yoshioka (2002)
Commentationes Mathematicae Universitatis Carolinae
In 1998, S. Romaguera [13] introduced the notion of cofinally Čech-complete spaces equivalent to spaces which we later called ultracomplete spaces. We define the subset of points of a space at which is not locally compact and call it an nlc set. In 1999, Garc’ıa-Máynez and S. Romaguera [6] proved that every cofinally Čech-complete space has a bounded nlc set. In 2001, D. Buhagiar [1] proved that every ultracomplete GO-space has a compact nlc set. In this paper, ultracomplete spaces which have...
On the tightness of chain-net spaces
István Juhász, William Weiss (1986)
Commentationes Mathematicae Universitatis Carolinae
On the *topology and its application
Hiroshi Hashimoto (1976)
Fundamenta Mathematicae
On the topology generated by preopen sets
D. Andrijević (1987)
Matematički Vesnik
On the weight of nowhere dense subsets in compact spaces.
Ivanov, A.V. (2003)
Sibirskij Matematicheskij Zhurnal
On thick spaces
M. Turzański (1976)
Colloquium Mathematicae
On thin-tall scattered spaces
I. Juhász, W. Weiss (1978)
Colloquium Mathematicae
On tightness in chain-net spaces
Ignacio Jané, Paul R. Meyer, Petr Simon, Richard Gordon Wilson (1981)
Commentationes Mathematicae Universitatis Carolinae
On topological and algebraic structure of extremally disconnected semitopological groups
Aleksander V. Arhangel'skii (2000)
Commentationes Mathematicae Universitatis Carolinae
Starting with a very simple proof of Frol’ık’s theorem on homeomorphisms of extremally disconnected spaces, we show how this theorem implies a well known result of Malychin: that every extremally disconnected topological group contains an open and closed subgroup, consisting of elements of order . We also apply Frol’ık’s theorem to obtain some further theorems on the structure of extremally disconnected topological groups and of semitopological groups with continuous inverse. In particular, every...
On topologies generated by some operators
Katarzyna Flak, Jacek Hejduk (2013)
Open Mathematics
The 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.
On topologies generating the Effros Borel structure and on the Effros measurability of the boundary operation
B. S. Spahn (1980)
Colloquium Mathematicae
On totally non-commutative convergence groupoids
Ján Šipoš (1989)
Mathematica Slovaca
On transfinite convergence and generalized continuity
Anna Neubrunnová (1980)
Mathematica Slovaca
On treelike neighbourhood spaces
R. Dimitrijević, Lj. Kočinac (1987)
Matematički Vesnik
On U-equivalence spaces
Farshad Omidi, MohammadReza Molaei (2015)
Topological Algebra and its Applications
In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U- equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.
On van Douwen spaces and retracts of
Alan S. Dow (2007)
Mathematica Bohemica
Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of . We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).
On weak forms of preopen and preclosed functions
Miguel Caldas, Govindappa Navalagi (2004)
Archivum Mathematicum
In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces.