Almost reflective subcategories of Top

AbstractThe concept of almost reflexive subcategories of is introduced, and it is shown that in the category Top of topological spaces and continuous maps the relations between the following concepts are rather tight: 1.(1) almost reflective subcategories2.(2) reflective subcategories3.(3) Implications subcategories (=injectivity classes),4.(4) orthogonal subcategories,5.(5) subcategories closed under the formation of products and retracts,6.(6) subcategories closed under the formation of limits,7.(7) subcategories A such that no space generates large A-spaces , The dual concepts are illuminated by examples in Top as well