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In 2000, Wang and He published an important result on the theory of intuitionistic fuzzy sets (IFSs). Indeed, they showed that every IFS may be regarded as an L‐fuzzy set for some appropriate lattice L. This paper aims to show that, nevertheless, the results obtained by various authors on intuitionistic fuzzy topological spaces (IFTSs), are not redundant with others for the ordinary fuzzy sense.

The most important definitions and results on intuitionistic fuzzy topology (IFT) one compared with the result obtained by Wang and He.

That these results are not redundant.

Clearly, this paper is devoted to IFTSs.

The main applications are in the mathematical field.

The originality and value of IFT are here demonstrated.

In 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non‐standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.

The paper investigates the possible relations between INSs and topology.

Relations on INSs and neutrosophic topology.

Clearly, the paper is confined to IFSs and NSs.

The main applications are in the mathematical field.

The paper shows original results on fuzzy sets and topology.

The purpose of this paper is to obtain an axiomatic characterization of Lowen's fuzzy compactness.

The paper shows a characterization of Lowen's fuzzy compactness.

The paper shows new results on fuzzy compactness.

Clearly, this paper is devoted to fuzzy topological spaces.

The main applications are in the mathematical field.

The paper presents original results on fuzzy topology.

To define some new kinds of fuzzy maps related with c‐zero dimensionality fuzzy, and various notions of fuzzy connectedness (due to Fatteh and Bassan, and Ajmal and Kohli, respectively), and obtain several properties about them.

The paper shows several properties of some new fuzzy maps.

The paper shows new results on fuzzy maps and various notios of fuzzy connectedness.

Clearly, this paper is devoted to fuzzy topological spaces.

The main applications are in the mathematical field.

The paper shows original results on fuzzy topology.

Recently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets (NSs). Also, this author introduced a general definition of neutrosophic topology. On the other hand, there exist various kinds of paraconsistent logics, where some contradiction is admissible. The purpose of this paper is to show that a Smarandache's definition of neutrosophic paraconsistent topology is not a generalization of Çoker's intuitionistic fuzzy topology (IFT) or Smarandache's general neutrosophic topology.

The possible relations between the IFT and the neutrosophic paraconsistent topology are studied.

Relations on IFT and neutrosophic paraconsistent topology are shown.

Clearly, the paper is confined to IFSs and NSs.

The main applications are in the mathematical field.

The paper shows original results on fuzzy sets and topology.

Recently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false.

The possible relation between the IFT and the neutrosophic topology is studied.

Relations on neutrosophic topology and IFT are found.

Clearly, this paper is confined to IFSs and NSs.

The main applications are in the mathematical field.

The paper shows original results on fuzzy sets and topology.

Recently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs) and also defined various notions of neutrosophic topologies on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and neutrosophic topologies on the non‐standard interval. The purpose of this paper is to show that this is false.

The possible relations between the intuitionistic fuzzzy topology and neutrosophic topologies are studied.

Relations on IFT and neutrosophic topologies.

Clearly, the paper is confined to IFSs and NSs.

The main applications are in the mathematical field.

The paper shows original results on fuzzy sets and topology.

D.Çoker constructed the fundamental theory of intuitionistic fuzzy topological spaces. The purpose of this paper is to introduce a new concept of compactness and a definition of paracompactness for intuitionistic fuzzy topological spaces, and obtain several preservation properties.

Two new covering properties in intuitionistic fuzzy topological spaces are defined and studied.

Relations on these new properties and covering properties on fuzzy topology in the Chang's sense are obtained.

Clearly, this paper is devoted to intuitionistic fuzzy topological spaces.

The main applications are in the mathematical field.

The paper shows original results on fuzzy topology.