## Are regular languages closed under homomorphism?

Regular languages are closed under inverse homomorphism, i.e., if L is regular and h is a homomorphism then h−1(L) is regular.

### Is homomorphism a Bijection?

An isomorphism of topological spaces, called homeomorphism or bicontinuous map, is thus a bijective continuous map, whose inverse is also continuous.

**Is regular set closed under complementation?**

The set of regular languages is closed under complementation. The complement of language L, written L, is all strings not in L but with the same alphabet.

**Are regular languages closed under reversal?**

4.2: The family of regular languages is closed under reversal.

## Are regular languages closed under subset?

Notice that regular languages are not closed under the subset/superset relation.

### What is the closure property of regular sets?

Closure properties on regular languages are defined as certain operations on regular language which are guaranteed to produce regular language. Closure refers to some operation on a language, resulting in a new language that is of same “type” as originally operated on i.e., regular.

**Are all isomorphisms bijective?**

All isomorphisms are bijections, but not vice- versa. Except in the category Set, where they coincide. Depending on the category, an isomorphism is a bijection which preserves the structure being studied.

**Are regular sets closed under union?**

1. Regular sets are closed under union,concatenation and kleene closure. Explanation: Regular sets are closed under these three operation.

## Are regular expressions closed under?

The regular languages are closed under complement, union, intersection, concatenation, and star. Proof The closure properties under union, concatenation, and star follow from the fact that the regular languages are those that are expressible with regular expressions.

### Are regular languages closed under all operations?

Closure refers to some operation on a language, resulting in a new language that is of same “type” as originally operated on i.e., regular. Regular languages are closed under following operations.

**Are regular languages closed under infinite intersection?**

The closure of regular languages under infinite intersection is, in fact, all languages. The language of “all strings except s” is trivially regular. You can construct any language by intersecting “all strings except s” languages for all s not in the target language.