https://www.um.edu.mt/library/oar/handle/123456789/143620 Wed, 08 Apr 2026 21:09:08 GMT 2026-04-08T21:09:08Z https://www.um.edu.mt/library/oar/handle/123456789/144070 Title: Intrinsic topologies on ordered structures : applications Abstract: This thesis is divided into two main parts. The first three chapters focus on the study of order and unbounded order convergence. We examine various well-established definitions of order convergence, that have emerged over time, each associated with a corresponding topology. These notions are compared in detail, with particular attention to the conditions under which they coincide or differ. Furthermore, in the context of a semi-finite measure space, we investigate the relationship between the topologies on L∞ arising from the duality (L∞, L1), and we compare these to the order topology. Notably, we establish a condition under which the Mackey topology is strictly weaker than the order topology. Compared to order convergence, unbounded order convergence is relatively new and is generally studied on Riesz spaces. In this thesis, we explore it in the broader context of lattices. Our results show that, similar to the order topology, the unbounded order topology is independent of the definition of order convergence. In addition, we extend key properties known to hold in Riesz spaces to lattices. We prove that order continuity of unbounded order convergence is equivalent to the lattice being infinitely distributive. Moreover, we show that the O-closure and uO-closure of a sublattice coincide and form a sublattice. Furthermore, we show that the uO-adherence of an ideal is an O-closed ideal. We also examine the MacNeille completion of a sublattice Y relative to that of a lattice L, identifying two conditions under which the completion of Y embeds regularly in that of L. The last chapter is dedicated to the study of lattice uniformities. It is known that for a locally solid Riesz space (X, τ ) there exists a locally solid linear topology uτ on X such that unbounded τ -convergence coincides with uτ -convergence. This topology is the weakest locally solid linear topology that agrees with τ on all order bounded subsets. Thus, for a uniform lattice (L, U), we introduce the weakest lattice uniformity U∗ on L that coincides with U on each order bounded subset of L. We see that if U is the uniformity induced by the topology of a locally solid Riesz space (X, τ ), then the U∗ -topology coincides with uτ . We also provide answers to several questions posed in [44, 37]. Description: Ph.D.(Melit.) Thu, 01 Jan 2026 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/144070 2026-01-01T00:00:00Z https://www.um.edu.mt/library/oar/handle/123456789/143652 Title: Integrating geophysical techniques and 3D modelling for lateral spreading : analysis and coastal risk mitigation in the Northern Region of ‘Rdum il-Qammieħ’ Abstract: This project investigates the geomorphological evolution and geohazard implications of coastal instability at ‘Rdum il-Qammieħ’, a prominent promontory on the northwestern coast of Malta. The study focuses on monitoring for lateral spreading which is a form of landslide where Upper Coralline Limestone detaches and slides over the underlying Blue Clay. This geological interface, compounded by regional tectonics and environmental forces, presents critical risks to both ecological and infrastructural assets. Based on Unmanned Aerial Vehicle photogrammetry, historical imagery, and Geographic Information System (GIS) tools, the research developed a high-resolution 3D model and an orthomosaic to map slope angles, block displacements, fracture mapping and surface deformations. CloudCompare and MeshLab helped in identifying high-risk zones marked by tension cracks, rotational slides, and seaward-tilted blocks. These physical indicators align with the region's structural framework, where structural discontinuities contribute to cliff segmentation and block mobility. A stereographic projection analysis confirmed a dominant South West dip direction (227°) and a strike of 137°, supporting interpretations of outward-tilting strata and block detachment patterns. The research further incorporates ecological assessments, highlighting how geomorphological processes threaten native species in Natura 2000 zones. Through hazard classification, the study delineates zones of critical, moderate, and low instability, offering a coastal risk map for use in policy and site management. A multi-temporal analysis was performed by georeferencing aerial photographs from 1964 to 2024, revealing long-term patterns of cliff retreat and block detachment. This historical mapping was validated using Root Mean Square (RMS) error thresholds, with lower values indicating higher georeferencing fidelity which is crucial for detecting subtle morphological changes over time. Observations noted, included back-tilted blocks, fracture mapping, and rockfall debris, confirm that the instability at ‘Rdum il-Qammieħ’ is both progressive and ongoing. Although large-scale collapses are currently infrequent, clear signs of incipient failure are evident, underscoring the need for continuous monitoring and informed intervention strategies The research offers an evaluation of terrain instability at ‘Rdum il-Qammieħ’, combining geomatics, geophysics, and ecological perspectives to inform proactive coastal risk management in Malta. Additionally, the findings contribute valuable insights into the mechanics of lateral spreading within Mediterranean karstic landscapes. Description: M.Sc.(Melit.) Thu, 01 Jan 2026 00:00:00 GMT https://www.um.edu.mt/library/oar/handle/123456789/143652 2026-01-01T00:00:00Z