Each covering induces a partition, such that every cover is union of partition classes, and it’s the coarsest between all partitions. This theorem is intuitively evident while the demonstration is not immediate.

Moreover any partition is topological base of cl-open topology, that is homeomorphic to some discrete topology.

The global increase in resistance to critically important antibiotics poses a serious public health threat, particularly due to mobile antibiotic resistance genes (ARGs) that facilitate rapid spread among bacteria through horizontal gene transfer. This study was conducted to assess antibiotic resistance genes and antibiotic resistance patterns in bacterial isolates from selected borehole water around open dump sites in the Onitsha South metropolis. Ten (10) borehole water samples were aseptically collected from ten (10) different boreholes 50 to 100m distance from the open dump sites and transported to Nnamdi Azikiwe University microbiology laboratory for microbial analysis. The membrane filtration method was used for the enumeration of total coliforms and fecal coliforms in the water samples, while serial dilution and pour plate methods were used for total heterotrophic bacterial counts. Bacterial isolates were identified based on cultural, morphological, and biochemical characteristics. Antibiotic susceptibility testing was carried out on the bacterial isolates using the Kirby-Bauer method, and results were interpreted in accordance with standard guidelines. The multiple antibiotic resistance (MAR) index was calculated for each isolate to assess antibiotic exposure levels. Antibiotic-resistant genes present in the MAR isolates were assessed by polymerase chain reaction (PCR) amplification of resistance genes (blaNDM, blaCTX-M, aac(6’)-Ib-cr ) followed by visualization by agarose gel electrophoresis. The isolates suspected in the water samples include Staphylococcus aureus (37.5%), Bacillus specie (25.0%), Vibrio specie, Staphylococcus specie,  and Escherichia coli are 8.3% respectively,  while Shigella specie, Klebsiella specie,  and Salmonella specie are 4.3% respectively. The results showed widespread bacterial contamination, with a high prevalence of multidrug resistance among isolates. Ceftazidime and Cefuroxime were resistant to 100% of the Gram-positive isolates while Levofloxacin was resistant to 63.2% of the Gram-positive isolates. All the antibiotics were resistant to 100% of the Gram-negative isolates except streptomycin which was resistant to 60% of the Gram-negative isolates. MAR index values ranged from 0.5 to 1.0, with 100% of the isolates showing values > 0.2, an indication of exposure to high-risk sources of contamination. PCR showed 100% detection of blaNDM in all the selected isolates, blaCTX-M was detected in 33.3% of the isolates selected, while aac(6')-Ib-cr was not detected in any of the isolate. This study calls attention to routine water quality monitoring, improved sanitation practices, and strict regulation of antibiotic use in Nigeria.

Background: Worldwide, modern land administration systems (LAS) are under unprecedented pressure due to rapid urbanization, the expansion of informal settlements, insecurity of tenures, environmental degradation, and inefficient maintenance of cadastral records. Although traditional ground-based methods of cadastral surveying provide legal precision at the millimeter level, they are too costly, require a great deal of labor, and are slow to carry out on a national scale.

Objective: This article gives a thorough and systematic summary of the newly developing geospatial technologies—these include photogrammetry using Unmanned Aerial Systems (UAS), Terrestrial and Mobile Light Detection and Ranging (LiDAR), Very High Resolution (VHR) Satellite Remote Sensing (SRS), the integration of 3D/4D Building Information Modeling with Geographic Information Systems (BIM-GIS), and Distributed Ledger Technology (Blockchain)—with regard to the modernisation of cadastral surveying and land governance.

Literature search and review method: A systematic literature search was carried out in Scopus, Web of Science, IEEE Xplore, and Google Scholar for peer-reviewed studies that were published between 2015 and 2026. The explicit inclusion criteria were used to select empirical investigations, technical frameworks, and policy evaluations relating to 2D/3D/4D cadastral modelling, fit-for-purpose land administration (FFPLA), and automated spatial data extraction.

Key findings: Compared with terrestrial techniques, integrated geospatial pipelines cut the time required for carrying out cadastral surveying in the field by 60 to 75 per cent and achieve horizontal and vertical positional accuracies at the centimetre level, meeting the statutory requirements for cadastral surveys. The use of active 3D sensor fusion (LiDAR-photogrammetry) together with BIM-GIS data integration overcomes the structural drawbacks of traditional 2D planar cadastres by allowing volumetric stratification of legal rights, restrictions, and responsibilities (RRRs). Moreover, decentralized ledgers incorporated with Spatial Data Infrastructures (SDI) greatly reduce instances of title corruption, boundary manipulation, and administrative friction.

Conclusion: Geospatial technologies form a fundamental basis for attaining the United Nations Sustainable Development Goals (SDGs 1, 11, and 15); in order to realise their full potential it is necessary to address the standardisation gaps in 3D data models (for example those in the Land Administration Domain Model ISO 19152), the high computational overheads, and the regulatory obstacles that exist in developing areas.

Successful implementation of curriculum reforms is highly dependent on teacher readiness, availability of teaching and learning resources, supportive learning environment and monitoring systems. After the updated pre-primary education curriculum was adopted in 2023, Tanzania Institute of Education (TIE) undertook a national monitoring exercise to evaluate its implementation in the Mainland Tanzania. The implementation of the revised curriculum was explored and key successes, issues and policy action points were captured. A cross sectional descriptive research design was adopted, whereby quantitative data was collected digitally using Kobo Toolbox from pre-primary education teachers in all 26 regions of Mainland Tanzania. The overall number of teachers involved in the study was 843. Data were analysed using descriptive statistics (frequency and percentage) and findings were interpreted in light of the contemporary literature on curriculum implementation. The results show promising advances in a number of areas. The majority of teachers had participated in training on the implementation of the curriculum, the teaching and learning of the curriculum was mostly learner-centred, and teachers were very innovative in creating teaching and learning materials which are available locally. However, there are still considerable implementation issues to address. Limitations of instructional resources, lack of teaching and learning materials, insufficient digital integration and uneven access to quality professional development were many of the schools' reports. Schools were perceived as safe places, but there were not enough facilities to adequately support competency-based learning. The study concludes that the revised pre-primary curriculum has laid a solid ground for its successful implementation in Tanzania, however, proper investment in teacher professional development, instructional materials, educational infrastructure and monitoring systems will be necessary to sustain successful implementation. The results will yield empirical evidence which can be used to inform policy, implementation, and future educational reforms in Tanzania and other developing countries. countries pursuing competency-based education.

Ensuring the authenticity of student identity during examinations remains a significant challenge in higher education, where conventional attendance procedures based on manual verification and examination slips are vulnerable to impersonation, administrative inefficiencies, and human error. This study presents an intelligent deep learning-based face recognition system developed to automate examination attendance management within the Faculty of Computing, Northwest University, Kano. The proposed system integrates Multi-task Cascaded Convolutional Networks (MTCNN) for robust face detection and alignment with FaceNet for discriminative facial feature embedding and identity recognition. To demonstrate its practical applicability, a web-based supervisor interface was developed to support real-time student authentication, automated attendance recording, secure storage of attendance records, and flexible attendance retrieval through student-based and course-based CSV reports. The proposed system utilized a facial image dataset collected from 69 registered students across four departments within the Faculty of Computing, Northwest University, Kano. Enrolment images were used to generate facial embeddings for each registered student, while the system was evaluated using 3,450 test images to assess its face recognition performance and practical applicability for examination attendance management. Experimental evaluation showed that the system correctly recognized 3,441 facial images, yielding an overall recognition accuracy of 99.74%, while achieving an average precision, recall, and F1-score of 0.99. Functional evaluation further confirmed the system's capability to perform reliable real-time attendance recording, prevent duplicate attendance entries, and efficiently generate attendance reports required for examination administration. Although recognition performance was influenced by variations in illumination and image quality, the overall findings demonstrate that the developed system provides an accurate, efficient, and practical biometric solution for strengthening examination attendance management and mitigating impersonation within the Faculty of Computing, Northwest University, Kano.