Some Questions on Metrizability
Some remarks about metric spaces, spherical mappings, functions and their derivatives.
If p ∈ Rn, then we have the radial projection map from Rn {p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a function in terms of its gradient, which can then be used to derive Sobolev inequalities, etc. In this paper...
Some remarks on shape properties of compacta
Some results on fixed points and their continuity
Some results on inverse spectra. II.
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 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.
Spaces of ANR's
Spaces of ANR's. II
Spaces of Seminorms.
Spaces with property
We prove that if is a first countable space with property and with a -diagonal then the cardinality of is at most . We also show that if is a first countable, DCCC, normal space then the extent of is at most .
Spaces With -Locally Finite Lindelöf sn-Networks
Squares of Q sets
Stability of convergent continuous descent methods.
Strict topology and perfect measures
Strongly metrizable spaces of large dimension each separable subspace of which is zero-dimensional
Sur le plongement d'un champ mesurable d'espaces métriques dans un champ trivial