A constructive proof of the Tychonoff's theorem for locales
A note on paratopological groups
In this paper, it is proved that a first-countable paratopological group has a regular -diagonal, which gives an affirmative answer to Arhangel’skii and Burke’s question [Spaces with a regular -diagonal, Topology Appl. 153 (2006), 1917–1929]. If is a symmetrizable paratopological group, then is a developable space. We also discuss copies of and of in paratopological groups and generalize some Nyikos [Metrizability and the Fréchet-Urysohn property in topological groups, Proc. Amer. Math....
A note on topological properties of non-Hausdorff manifolds.
A universal property of -semigroups
Let be a -semigroup with unbounded generator . We prove that has generically a very irregular behaviour for as .
Another look at the localic Tychonoff theorem
Cauchy sequences in -groups
Characterizations of certain general and reproductive solutions of arbitrary equations
Characterizing polyhedrons and manifolds
In [5], W. Taylor shows that each particular compact polyhedron can be characterized in the class of all metrizable spaces containing an arc by means of first order properties of its clone of continuous operations. We will show that such a characterization is possible in the class of compact spaces and in the class of Hausdorff spaces containing an arc. Moreover, our characterization uses only the first order properties of the monoid of self-maps. Also, the possibility of characterizing the closed...
Coarse homotopy on metric spaces and their corona
This paper discusses properties of the Higson corona by means of a quotient on coarse ultrafilters on a proper metric space. We use this description to show that the corona functor is faithful and reflects isomorphisms.
Compactness and Tightness in a Space of Measures with the Topology of Weak Convergence.
Compactness type properties in topological groups
Computing complexity distances between algorithms
We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement...
Continuous relations and generalized sets
Example of a convergence commutative group which is not separated
First order topology [Book]
Intégration non archimédienne
Isomorphismen, topologische Maßräume.
Isomorphisms of products
Menger's Theorem for topological spaces
Neighborhood base at the identity of free paratopological groups
In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.