Summands in locally almost square and locally octahedral spaces

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Almost Factorizable Locally Inverse Semigroups

A factorizable inverse monoid can be identified, up to isomorphism, with an inverse submonoid M of a symmetric inverse monoid I(X) where each element of M is a restriction of a permutation of X belonging to M . So factorizable inverse monoids are natural objects, and appear in a number of branches of mathematics, cf. [12], [4]. The notion of an almost factorizable inverse semigroup was introduc...

Locally Compact, Locally Countable Spaces and Random Reals

In this note I will present a proof that, assuming PFA, if R is a measure algebra then after forcing with R every uncountable locally compact locally countable cometrizable space contains an uncountable discrete set. The lemmas and techniques will be presented in a general form as they may be applicable to other problems.

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

Locally Compact Path Spaces

It is shown that the space X [0,1], of continuous maps [0, 1] → X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T1-space X, it follows that X [0,1] is locally compact if and only if X is locally compact and totally path-disconnected. AMS Classification: 54C35, 54E45, 55P35, 18B30, 18D15