Senior Lecturer

Qualifications:

• Bsc Physics, University of the Western Cape
• Bsc Honours in Physics (Cum Laude), University of the Western Cape
• MSc (Pure) Mathematics (Cum Laude), University of the Western Cape
• PhD (Pure) Mathematics, University of South Africa

Contact Details:

m.nxumalo@ru.ac.za, Room 2 Maths Building (Drostdy Lodge), (046) 603 7485

Teaching:

• Calculus (In MAM101): Basic concepts (number systems, functions), calculus (limits, continuity, differentiation, curve sketching, introduction to integration),
  
  
• Introduction to Analysis (In MAM202): Real numbers; open and closed intervals; sequences and series (convergence); functions of a real variable (continuity, limit); series of functions; Taylor series.
  
  
• Topology (In MAT315): Revision on sets and functions; topological spaces (fundamental concepts, closure, interior, neighborhood, subspaces, bases and continuity); lower separation axioms (T0, T1 and T2).
  
  
• Category Theory: An honours course that reveals how different pure mathematics structures are related to one another. For instance, topological spaces, groups, rings and sets.
  
  
• Topology: An honours course that covers the topics: Finite products of spaces; Infinite products of spaces; Quotient spaces; Topological convergence (via filters and ultrafilters); Separation axioms (regular, completely regular, Tychonoff and normal spaces); Urysohn's lemma; Compactness (compact spaces, locally compact spaces and compactifications); The Tychonoff theorem; Metrizable spaces; Connectedness (connected spaces, pathwise connectedness, local connectedness); The fundamental group (homotopy, the fundamental group).

Research Interests:

• General Topology
• Point-Free Topology (Locale and Frame Theory)
• Categorical Topology
• Topological Data Analysis*

Honours Projects:

My research interest is in pure mathematics with topics in general topology, locale theory and frame theory. I use categorical notions to extend work in the mentioned topics.

Publications:

• Ngcamphalala T. and Nxumalo M., 2025. B-normality in locales. Applied General Topology,  26 (1), 543-574.
• Nxumalo M., 2025. Some variants of remote sublocales. Filomat, 39 (8), 2587–2601.
• Nxumalo M., 2025. On the category of (i,j)-Baire bilocales. European Journal of Pure and Applied Mathematics 18 (1), 5362
• Nxumalo M., 2024. Remoteness in the category of bilocales. Filomat, 38(22).
• Nxumalo, M., 2024. On maximal nowhere dense sublocales. Applied General Topology, 25(2), 331-361.
• Nxumalo, M., 2024. On open maps and related functions over the Salbany compactification. Archivum Mathematicum, 60(1), pp.21-33.
• Nxumalo, M., 2023. Remote sublocales. Quaestiones Mathematicae, 47(6), pp.1177-1194.

Media Release:

1. 2020 University of the Western Cape: ``Class Of 2020: Mbekezeli Sibahle Nxumalo On The Shape Of Things - And His Undying Love For Mathematical Topology''
2. Patient teacher helped Nxumalo to love maths

Last Modified: Fri, 25 Apr 2025 08:35:21 SAST