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## Proyecciones (Antofagasta)

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*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.28 no.1 Antofagasta May 2009

#### http://dx.doi.org/10.4067/S0716-09172009000100001

Vol. 28, Nº 1, pp. 1-19, May 2009.

Universidad Católica del Norte

Antofagasta - Chile

ON ĝ-HOMEOMORPHISMS IN TOPOLOGICAL SPACES

**M. CALDAS**

^{1}

**S. JAFARI**

^{2}

**N. RAJESH**

^{3}

**M. L. THIVAGAR**

^{4}

^{1}Universidade Federal Fluminense, Brasil.

^{2}College of Vestsjaelland South, Denmark.

^{3}Ponnaiyah Ramajayam College, India.

^{4}Arul Anandhar College, India.

Correspondencia a:

**Abstract**

In this paper, we first introduce a new class of closed map called ĝ-closed map. Moreover, we introduce a new class of homeomorphism called ĝ-homeomorphism, which are weaker than homeomorphism. We prove that gc-homeomorphism and ĝ-homeomorphism are independent. We also introduce ĝ*-homeomorphisms and prove that the set of all ĝ*-homeomorphisms forms a group under the operation of composition of maps.

**2000 Math. Subject Classification :**54A05, 54C08.

**Keywords and phrases :**ĝ-closed set, ĝ-open set, ĝ-continuous function, ĝ-irresolute map.

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**M. CALDAS**

Departamento de Matemática Aplicada

Universidade Federal Fluminense

Rua Mário Santos Braga, s/n^{o}

24020-140, Niterói

RJ BRAZIL

e-mail : __gmamccs@vm.uff.br__

**S. JAFARILI**

College of Vestsjaelland South

Herrestraede 11

4200 Slagelse

DENMARK

e-mail : __jafari@stofanet.dk__

**N. RAJESH **

Department of Mathematics

Ponnaiyah Ramajayam College

Thanjavur, TamilNadu

INDIA

e-mail : __nrajesh.topology@yahoo.co.in__

**M. L. THIVAGAR**

Department of Mathematics

Arul Anandhar College

Karumathur, Madurai, TamilNadu

INDIA

e-mail : __mlthivagar@yahoo.co.in__

*Received : August 2006. Accepted : November 2008*