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Definition of S-Reducibilityreducibility and Reducibilityreducibility of a Spacespace

I was going through this paper by Tanaka but I am stuck at the Proposition 4.1 given below enter image description here. I just cannot make sense of the first two lines of the proof. What does it mean when he says S-reducible and reducible? I tried searching online also but could not find anything, nor does the author refer to anything.

Can someone help me with this?

Thanks and regards in advance.

Definition of S-Reducibility and Reducibility of a Space

I was going through this paper by Tanaka but I am stuck at the Proposition 4.1 given below enter image description here. I just cannot make sense of the first two lines of the proof What does it mean when he says S-reducible and reducible? I tried searching online also but could not find anything, nor does the author refer to anything.

Can someone help me with this?

Thanks and regards in advance.

Definition of S-reducibility and reducibility of a space

I was going through this paper by Tanaka but I am stuck at Proposition 4.1 given below enter image description here. I just cannot make sense of the first two lines of the proof. What does it mean when he says S-reducible and reducible? I tried searching online also but could not find anything, nor does the author refer to anything.

Can someone help me with this?

Thanks and regards in advance.

Source Link

Definition of S-Reducibility and Reducibility of a Space

I was going through this paper by Tanaka but I am stuck at the Proposition 4.1 given below enter image description here. I just cannot make sense of the first two lines of the proof What does it mean when he says S-reducible and reducible? I tried searching online also but could not find anything, nor does the author refer to anything.

Can someone help me with this?

Thanks and regards in advance.