The Lusternik-Schnirelman categories of a product space
Compositio Mathematica, Tome 22 (1970) no. 2, pp. 175-180. 
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     author = {Takens, Floris},
     title = {The {Lusternik-Schnirelman} categories of a product space},
     journal = {Compositio Mathematica},
     pages = {175--180},
     publisher = {Wolters-Noordhoff Publishing},
     volume = {22},
     number = {2},
     year = {1970},
     mrnumber = {290365},
     zbl = {0198.28302},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1970__22_2_175_0/}
}
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Takens, Floris. The Lusternik-Schnirelman categories of a product space. Compositio Mathematica, Tome 22 (1970) no. 2, pp. 175-180. http://archive.numdam.org/item/CM_1970__22_2_175_0/

R.H. Fox [1] On the Lusternik-Schnirelman category, Annals of Math. 42 (1941) 333-370. | JFM | MR | Zbl

T. Ganea [2] Lusternik-Schnirelman category and strong category, Ill. Journal of Mathematics 11 (1967) 417-427. | MR | Zbl

J. Milnor [3] On spaces having the homotopy type of a C.W. complex. Trans. Amer. Math. Soc. 90 (1959) 272-280. | MR | Zbl