We show that it is consistent relative to a weakly compact cardinal strong homology additive and compactly supported within the class of locally separable metric spaces. This complements work Mardešić Prasolov [14] showing Continuum Hypothesis implies countable sum Hawaiian earrings witnesses failure possess either these properties. Our results build directly on Lambie-Hanson second author [3] ...

Inspired by work of Lipshitz-Sarkar, we show that the module structure on link Floer homology detects split links. Using results Ni, Alishahi-Lipshitz, and establish an analogous detection result for sutured homology.

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...