MODIFIED FORMS OF SOFT NANO CONTRA CONTINUOUS FUNCTIONS

The objective of this paper is to present two such contexts where the results obtained for soft nano contra continuous functions widely differ from those known for soft nano continuous functions. Significant facts concerned with soft nano contra continuous, soft nano contra g -continuous, soft nano contra g -irresolute functions, maps, soft nano almost contra g continuous functions are developed. Also, the stronger forms of soft nano contra continuous and soft nano contra g -continuous functions called the soft nano-bi-contra continuous functions, soft nano-bi-contra g continuous functions. Soft nanostrongly-bi-contra g continuous functions are studied with their notable properties.


Remark 3.8:
The converse of the theorem 3.7 need not be true in general. ii) every soft nano contra strongly -continuous is soft nano contra continuous.
iii) every soft nano contra strongly -continuous is soft nano contra -continuous. iv) every soft nano contra strongly -continuous is soft nano contra -irresolute.
ii) Let ( ) as a sn-O( ) and it is sn--O( ) [17]. Here iii) Follows from the fact that every soft nano contra continuous function is soft nano contra continuous, the proof is obvious iv) Obvious.

Remark 3.11:
Composition of two soft nano contra g -continuous functions is a soft nano contra g -continuous function  ii) -c-wg-continuity and --continuity are independent concepts.
The following examples are proposed to show that the above statements are valid. Here is -c--continuous but not -continuous. ii) is sn-c--irresolute and is sn--irresolute, then is sn-c-g -irresolute.

SOFT NANO
iii) is sn--irresolute and is sn-c-continuous, then is sn-c-g -continuous.
v) is sn-c--continuous and is sn-continuous, then is sn-c-g -continuous.

SOFT NANO ALMOST CONTRA g -CONTINUOUS FUNCTIONS
In this section, soft nano almost contra g -continuous functions are introduced and their properties are studied. Proof: Let ( ) be sn-r-C( ). As is sn-almost-contra-g -continuous, Hence is sn-almost-contra-g -continuous.
1186 MODIFIED FORMS OF SOFT NANO CONTRA CONTINUOUS FUNCTIONS Theorem 6.4: Let is soft nano-almost-contra-gcontinuous and is soft nano-almost-contra-gcontinuous, then soft nano-almost-contra-g -continuous.
Theorem 6.5: Let is soft nano-almost contra gcontinuous and is soft nano perfectly continuous, then soft nano-contra-g -continuous.
Theorem 6.6: Let is soft nano-almost contra gcontinuous and is -map, then soft nanoalmost-contra-g -continuous.

SOFT NANO-BI-CONTRA-CONTINUOUS FUNCTIONS
. Therefore is soft nano bi-contra continuous function. is sn-bi-contra continuous map.
Proof: By hypothesis is sn-bi-contra continuous. Let be sn-O( ), then is sn-O( ). Since is sn-contra continuous. As is clopen, is sn-C . Here = .
Since is sn-clopen, is sn-O( ) and as is sn-bi-contra continuous is sn-C( ). Theorem 8.2: Every soft nano-bi contra continuous is soft nano bi-contra g -continuous.
Proof: Let be sn-O( ). We know that soft nano-contra-continuous implies soft-nano-contra-g -continuous. As is soft nano-bi-contra-continuous, is soft nanog -closed in .Therefore, is soft nano-g -C( ).

Remark 8.3:
The converse of above theorem is not true always. Hence is not sn-bi-contra continuous map.

Theorem 8.5:
If is onto, soft-nano-contra gcontinuous and soft nano-contra g -open, then is soft nano-bi-contra g -continuous.

Theorem 8.6:
Let be an open surjective, sn-girresolute and be a soft nano-bi-contra gcontinuous map. Then is soft nano-bi-contra g -continuous map.

Theorem 8.7:
If is soft nano-bi-contra gcontinuous map and is a continuous map, where is a space that is constant on each set ({( , )}), for ( , ) , then induces a soft nano-bi-contra g -continuous map such that = .

SOFT NANO STRONGLY-BI-CONTRA g -CONTINUOUS MAPS
Definition 9.1: Let be an onto map. Then is called a soft nano strongly-bi-contra g -continuous provided is soft nano contra g -continuous and is soft nano open in , if and only if is soft nano g -closed in . is an soft nano-bi-contra-(g )*-continuous.