$L$-guilds and Binary $L$-merotopies

Mona Khare, Rashmi Singh

The present paper is primarily concerned with the study of$L$-guilds in an$L$-merotopic space. It is shown that every$L$-cluster is an$L$-guild; however the converse is not true. For contigual and regular$L$-merotopies, where on one side we gave an example of a space, which is neither contigual nor binary, on the other side we constructed$L$-merotopic spaces that are contigual and binary. It is shown that the category LBIN of binary$L$-merotopic spaces and$L$-merotopic maps is bireflective in LMER, the category of$L$-merotopic spaces and$L$-merotopic maps.