There are absolute ultrafilters on N which are not minimal
There is no universal separable Fréchet or sequential compact space
Tightness and resolvability
We prove resolvability and maximal resolvability of topological spaces having countable tightness with some additional properties. For this purpose, we introduce some new versions of countable tightness. We also construct a couple of examples of irresolvable spaces.
Tightness and π-character in centered spaces
We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the centered...
Tightness of compact spaces is preserved by the -equivalence relation
We prove that if there is an open mapping from a subspace of onto , then is a countable union of images of closed subspaces of finite powers of under finite-valued upper semicontinuous mappings. This allows, in particular, to prove that if and are -equivalent compact spaces, then and have the same tightness, and that, assuming , if and are -equivalent compact spaces and is sequential, then is sequential.
Topological calculus for separating points from closed sets by maps
Pointfree formulas for three kinds of separating points for closed sets by maps are given. These formulas allow controlling the amount of factors of the target product space so that it does not exceed the weight of the embeddable space. In literature, the question of how many factors of the target product are needed for the embedding has only been considered for specific spaces. Our approach is algebraic in character and can thus be viewed as a contribution to Kuratowski's topological calculus.
Topological characterization of the small cardinal
We show that the small cardinal number is a maximal independent family} has the following topological characterization: has a dense irresolvable countable subspace}, where denotes the Cantor cube of weight . As a consequence of this result, we have that the Cantor cube of weight has a dense countable submaximal subspace, if we assume (ZFC plus ), or if we work in the Bell-Kunen model, where and .
Topological completeness of first countable Hausdorff spaces II
Topological completeness of first countable Hausdorff spaces I
Topological spaces with a selected subset-cardinal invariants and inequalities
Cardinal functions for topological spaces in which a subset is selected in a certain way are defined and studied. Most of the main cardinal inequalities are generalized for such spaces.
Topologie fine et mesure de référence.
Topologies generated by closed intervals.
Total negation under constraint: pre-anti properties
L'operazione «anti( )» di Paul Bankston fu introdotta in contesto della famiglia di tutti gli spazii topologici. Però, per molte ricerche ci conviene lavorare esclusivamente in una classe costretta di spazii di cui la struttura e ricca abbastanza di facilitare il ragionamento. In quest'articolo descriviamo come trasferire anti ( ), e concetti allacciati, dentro una tale classe costretta; con riferimento speciale all'esistenza di «pre-antis».
Totally divergent dense sets in Cantor cubes
Two cardinal inequalities for functionally Hausdorff spaces
In this paper, two cardinal inequalities for functionally Hausdorff spaces are established. A bound on the cardinality of the -closed hull of a subset of a functionally Hausdorff space is given. Moreover, the following theorem is proved: if is a functionally Hausdorff space, then .
Two examples of non-separable metrizable spaces
Two examples of pseudo-radial spaces
Two improvements on Tkačenko's addition theorem
We prove that (A) if a countably compact space is the union of countably many subspaces then it is compact; (B) if a compact space is the union of fewer than = left-separated subspaces then it is scattered. Both (A) and (B) improve results of Tkačenko from 1979; (A) also answers a question that was raised by Arhangel’skiǐ and improves a result of Gruenhage.
Two-valued measure need not be purely -compact
Ueber einen Satz aus der Theorie der stetigen Mannigfaltigkeiten