This is a glossary of some terms used in the branch of mathematics known as topology. Although there is no absolute distinction between different areas of topology, the focus here is on general topology. The following definitions are also fundamental to algebraic topology, differential topology and geometric topology.
See the article on topological spaces for basic definitions and examples, and see the article on topology for a brief history and description of the subject area. See Naive set theory, Axiomatic set theory, and Function for definitions concerning sets and functions. The following articles may also be useful. These either contain specialised vocabulary within general topology or provide more detailed expositions of the definitions given below. The list of general topology topics and the list of examples in general topology will also be very helpful.
All spaces in this glossary are assumed to be topological spaces unless stated otherwise.
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Here are some facts about submaximality as a property of topological spaces:
 Every door space is submaximal.
 Every submaximal space is weakly submaximal viz every finite set is locally closed.
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