Foundations of Topology

0. Preliminaries.- 0.1 Set theoretical concepts.- 0.2 Topological structures.- 0.3 Some categorical concepts.- 1. Topological constructs.- 1.1 Definition and examples.- 1.2 Special categorical properties of topological constructs.- 2. Reflections and coreflections.- 2.1 Universal maps and adjoint functors.- 2.2 Characterization theorems of ?-reflective and M-coreflective subcategories.- 2.3 Examples of bireflections and bicoreflections.- 3. Topological universes.- 3.1 Cartesian closed topological constructs.- 3.2 Extensional topological constructs.- 3.3 Strong topological universes.- 4. Completions of semiuniform convergence spaces.- 4.1 Completion of uniform spaces.- 4.2 Regular completion of semiuniform convergence spaces.- 4.3 Applications to compactifications.- 4.4 The simple completion and the Wyler completion.- 5. Connectedness properties.- 5.1 Connectednesses.- 5.2 Disconnectednesses and their relations to connectednesses.- 5.3 Local ?-connectedness.- 6. Function spaces.- 6.1 Simple convergence, uniform convergence and continuous convergence in the realm of classical General Topology.- 6.2 Local compactness and local precompactness in semiuniform convergence spaces.- 6.3 Precompactness and compactness in the natural function spaces of the construct of semiuniform convergence spaces.- 7. Relations between semiuniform convergence spaces and merotopic spaces (including nearness spaces).- 7.1 An alternative description of filter spaces in the realm of merotopic spaces.- 7.2 Subtopological spaces.- 7.3 Complete regularity and normality.- 7.4 Paracompactness and dimension.- 7.5 Subcompact and sub-(compact Hausdorff) spaces.- Appendix. Some algebraically topological aspects in the realm of Convenient Topology.- A.l Cohomology for filter spaces.- A.2 Path connectednessand fundamental groups for limit spaces.- Exercises.- Implication scheme for various SUConv-invariants.- Table: Preservation properties of some SUConv-invariants.- Diagram of relations between various subconstructs of SUConv (including their relations to merotopic and nearness spaces).- List of axioms.- List of symbols.