What is the meaning of Proper?

Suitable.

1. Suited or acceptable to the purpose or circumstances; fit, suitable.

   Suited or acceptable to the purpose or circumstances; fit, suitable.

   Following the established standards of behavior or manners; correct or decorous.

   Such that the preimage of every compact set is compact.

   Continuous, mapping closed sets to closed sets, and such that the preimage of every point is compact.

   separated, of finite type, and universally closed.

   such that unique morphism from the variety to ${\displaystyle k}$ is proper (as above).

   Such that every closed ball is compact

   Possessed, related.

   1. Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter.
   2. Pertaining exclusively to a specific thing or person; particular.
   3. In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).
   4. Belonging to oneself or itself; own.

      Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter.

      Pertaining exclusively to a specific thing or person; particular.

      In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).

      Belonging to oneself or itself; own.

      Portrayed in natural or usual coloration, as opposed to conventional tinctures.

      Being strictly part of some other thing (not necessarily explicitly mentioned, but of definitional importance), and not being the thing itself.

      Eigen-; designating a function or value which is an eigenfunction or eigenvalue.

      Accurate, strictly applied.

      1. Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.)

         Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.)

         Attractive, elegant.

         In the very strictest sense of the word.

         Utter, complete.

         Not being a set.

         properly; thoroughly; completely.

         properly.

         Something set apart for a special use.

         A part of the Christian liturgy that varies according to the date.

         near, close

         neighbouring

         next

         second-person singular imperative of proprat

         cleanly

         tidy

         clean

         in good condition: clean; neat; well-kept; developed

         overweight; chubby

         Alternative form of propre

         neat, tidy

         proper (following (strict) established social standards)

         Source: wiktionary.org