Some results on groups with unique square roots
Some results on inverse spectra. II.
Some results on -spaces
We present several results related to -spaces where is a finite cardinal or ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.
Some results on metric trees
Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree (T, d) is a metric space such that between any two of its points there is a unique arc that is isometric to an interval in ℝ. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images x₀ = π((x₁ + ... + xₙ)/n), where π is a contractive...
Some results on semi-stratifiable spaces
We study relationships between separability with other properties in semi-stratifiable spaces. Especially, we prove the following statements: (1) If is a semi-stratifiable space, then is separable if and only if is ; (2) If is a star countable extent semi-stratifiable space and has a dense metrizable subspace, then is separable; (3) Let be a -monolithic star countable extent semi-stratifiable space. If and , then is hereditarily separable. Finally, we prove that for any -space...
Some results on spaces with -calibre
We prove that, assuming CH, if is a space with -calibre and a zeroset diagonal, then is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with -calibre.
Some results on uniform spaces with linearly ordered bases
Some sequential properties
Some similarity between contractions and Kannan mappings.
Some topological consequences of the Product Measure Extension Axiom
Some versions of second countability of metric spaces in ZF and their role to compactness
In the realm of metric spaces we show in ZF that: (i) A metric space is compact if and only if it is countably compact and for every , every cover by open balls of radius has a countable subcover. (ii) Every second countable metric space has a countable base consisting of open balls if and only if the axiom of countable choice restricted to subsets of holds true. (iii) A countably compact metric space is separable if and only if it is second countable.
Some weak forms of continuity in bitopological spaces
Space structures, their theory and application. II.
Spaces of ANR's
Spaces of ANR's. II
Spaces of retractions which are homeomorphic to Hilbert space
Spaces of Seminorms.
Spaces whose only finite-sheeted covers are themselves. I.
Spaces with a locally countable -network.
Spaces with a primitive base and perfect mappings